Okay, so you need to learn from what is going on right now...And I'm not saying this to be a smart-ass or to be mean/nasty to you, but to really get you thinking about this so you don't keep making the same exact mistake and have to keep going through this same problem over and over and over again like some people do...Well, a lot of people do because they just don't get it, or they just won't listen...
First of all, yes, please give one of your Budgies to your friend IMMEDIATELY if you just cannot make space for a second table-top cage right now, I hate to see that happen to you (NOT TO THEM, TO YOU, THEY DON'T LIKE EACH OTHER AND DON'T WANT TO SHARE THEIR "TERRITORY" WITH EACH OTHER, SO YES, THEY'LL NOT ONLY BE FINE BEING LONE-BIRDS, BUT THEY'LL BE MUCH HAPPIER BIRDS, BOTH OF THEM!)...But if that's all you can do then you need to pack one of them up, make sure your friend has an adequate cage for them or you buy one for them ASAP, make sure your friend knows their regular, daily diet, treats, cage cleaning, and sleep-schedule, etc., and GET THEM SEPARATED IMMEDIATELY BEFORE ONE OF THEM IS SERIOUSLY INJURED OR KILLED! I know you're trying to "watch them", but you can't watch them 24 hours a day, and it only takes literally one second for one of them to lose an eye, have their entire beak ripped-off (this happens quite often, one of the most common injuries resulting from two Budgies fighting is one of them getting their entire upper-beak ripped off of their face, and they don't grow-back, so the poor thing has a literal hole in it's face for the rest of it's life and can no longer eat seeds!)...They actually also quite often end-up ripping each other's heads off, no joke or exaggeration, Budgies who are aggressive/violent and fighting don't ever stop, whether it's due to hormones or due to them just simply hating each other, or jealousy over sharing a territory (their cage), it won't ever stop and will progressively escalate a little each day until one day you come home and find something horrible and traumatic, and that might cost you thousands of dollars at the Avian Vet...So you can't keep them living together any longer no matter how you try to "watch them...And just to point something out to you, if there is any way you can find the little space for a second table-top cage so you can keep them (HANG IT FROM THE CEILING! OR BUY A LITTLE WIRE FLOOR-STAND TO HANG IT FROM!), they might be totally fine once you separate them into their own, individual cages because their aggression/fighting might be due to jealousy of territory sharing. If you separate them into their own cages but keep them in the same room so they can see each other and talk to each other, they may likely be totally fine when they are allowed out of their respective cages together, they might snuggle and preen each other...Then again, they might try to kill each other when outside of their own, individual cages too, YOU JUST DON'T KNOW UNTIL YOU TRY IT...
****However, if you really just can't make room for a second table-top/hanging cage to separate them into immediately, then you absolutely need to get them separated somehow immediately before something horribly bad happens...And if your friend will take one of them, then please make that happen immediately...
But here's the issue...You're already talking about going out and buying ANOTHER BUDGIE TO PUT INSIDE THE SAME CAGE AS THE ONE YOU KEEP???? WHY WOULD YOU EVEN THINK ABOUT DOING THAT???? Seriously, again I'm not trying to be mean, rude, nasty, or a smart ass, but trying to get you thinking about his situation...You already know you can't find room for a second cage in your current apartment, right? So you actually are thinking about going out, buying another new Budgie, bringing it home, and putting it inside of the same cage as the Budgie you already have??? Even though you are having to separate the second Budgie you have now because they are fighting and going to badly hurt or kill each other??? Think about that for a second...
***Your 2 current Budgies are not fighting because they are both females. Not at all. And going out and buying a new, second Budgie that's a male to put in with the one female you keep is likely going to end exactly the same way as this situation is, or even possibly much more tragically. So the ONLY WAY you can bring home a second bird of any species, sex, size, etc. is if you also buy a second cage at the same time as you buy the second bird and you make room in your apartment to put the second bird in. That's it, that's the only way you can do this...YOU CANNOT EVER, EVER, EVER, JUST BRING HOME A SECOND BIRD/PARROT AND PUT THEM RIGHT INTO THE CAGE THAT YOU ALREADY HAVE A CURRENT BIRD IN!!!
And that is for multiple reasons...In addition to the fact that they don't know each other at all and they might kill each other in a matter of seconds after you put the new bird inside of your current bird's cage, but there is also the fact that you have to do a 30-day quarantine of any new bird you bring home, in a totally other room behind a closed door away from your current bird, just in-case the bird you bring home has some horrible Avian Viral Disease like Parrot Beak-and-Feather Disease (PBFD), Avian Borna-Virus (ABV), etc. And that's forgetting bacterial and/or fungal/yeast infections, mites infestations (very common with Budgies), worms and other parasites, etc. So you can't just bring home a new bird and throw it in the same cage as your current bird, more-so because you have no idea how they are going to interact with each other, what type of relationship/bond they will have, how they are going to react about sharing a territory/cage, or about sharing anything else, like YOU, or your home...
Birds/Parrots for relationships with each other much like we as people do. And the fact of the matter is that you have absolutely NO IDEA what type of relationship any new bird you bring home will have with your current Budgie (the one you keep I mean). And there is absolutely NO GUARANTEE AT ALL that they will even be able to be out together out of their cages in your apartment, let alone be able to live in the same cage together, and that's after a few months of them living together and getting to know each other!!! So you obviously cannot just bring home a second bird, throw it in the same cage as your current bird, and have everything be okay. Because it will no be okay,
Two birds might love each other and want to share a cage, they might love each other but not be alright with sharing a cage/territory, they might simply tolerate each other but not really want much to do with each other, they might really dislike each other and want to stay far away from each other, they might really, really hate each other and fight any time they get close to one another, and they might hate each other so much that they aggressively go after each other and purposely try to kill each other...And you have no way at all of know how that is going to end-up, and you won't until you've done the 30-day quarantine in another room with the new bird, then you move the new bird's separate cage into the same room as your current bird and you let them see each other, talk to each other, and get to know each other over a matter of months, by letting them out under direct-supervision as often as you can to see how they get along and whether or not they form any type of bond over-time.
So the bottom-line is that unless you can fit a second adequately-sized cage in your current apartment, you will not be able to get a second bird!!! Nor should you really, because YOU are your current Budgie's Flock-Mate, her Friend, her Companion, and her Family!!! She doesn't need "a new friend" because obviously she may not want a new friend, and you'll be right back where you are now again...So just concentrate on forming a bond with whichever Budgie you decide to keep, work on training her, taming her, teaching her Recall-Training and Target Training, and why not even order her an Aviator-Harness and spend a good couple of months training her daily to accept putting it on and wearing it, and then you can take her out with you places??? Budgies have the intelligence of a 2-3 year-old human child, and they are extremely affectionate, snuggly, cuddly, loving little parrots, ESPECIALLY IF YOU HAVE ONLY A SINGLE, LONE BUDGIE!!! That's the perfect situation to make your relationship and bond with whatever Budgie you keep really special...My first Budgie, who my mom bred/hand-raised and gave me when I was 6 years-old, was my best-friend in the world, he went everywhere with me, he was my only pet, and he lived to be 18 years and 9 months old!!! He went away to college with me!!! So that's the kind of relationship you COULD HAVE with whatever Budgie you keep, and you'll not have to worry about again having 2 birds in your apartment that hate each other and are hurting each other...
*****Also, just an FYI that I don't think you've thought about either, is the fact that if you go out and buy a second MALE Budgie to immediately put in the SAME CAGE as your current FEMALE Budgie, if they do happen to actually like each other and bond with each other, YOU WILL HAVE A CHRONIC BREEDING ISSUE, as well as a probably CHRONIC EGG-LAYING FEMALE, which unfortunately is extremely common once a Female Budgie starts laying eggs, whether they are fertile or not...So forgetting that you obviously have no room at all for a Brooder or multiple weaning-cages for babies, which you'd have no choice at all about getting and having, but you could very well end-up with your Female becoming a chronic egg-layer, which is very harmful to their health and often ends in their early, sudden death from either Egg-Binding or Malnutrition/Calcium and/or Phosphorous Deficiency...So bringing home a second MALE Budgie to put right immediately inside your current Female's cage is a horrible idea for many, many reasons...