Welcome to the forum! Let's see if we can help you at least find the closest Avian or even a Poultry Vet to you...in the meantime, can I ask you some questions about your Budgie?
I'm assuming that this is a Budgie that you have used as a breeder? Is that correct?
How old is she now? How many clutches has she laid in her lifetime? And when did she lay the last one that she started acting this way after?
Has she also been breathing heavily since this started? Panting, like a dog pants? And you said she's visibly thin, correct?
What is Mint's daily diet?
First of all, it's very important that you not breed Mint again, as this happens to female Budgies often after they have become extremely stressed after laying too many eggs...So the first thing you need to is make certain that she has no more clutches, which means that you must separate her from the male Budgie she has been mating with. They can stay in cages next to each other so they can still see each other, but they cannot be in the same cage anymore, as it's likely to kill her if she mates again...
Also, it's extremely important that she is getting ample water, ample food (hopefully pellets, seeds, and fresh veggies every single day)...adding EggFood to her daily diet is also going to help, and you can make this yourself if you can't buy it in a pet shop where you live, you simply cook her some scrambled eggs, but you must grind-up the shells finely and add them into the eggs...And she also needs to have access all the time to a Cuttlebone/Mineral Block, as she is most-likely suffering from not only malnutrition in-general, but also a severe Calcium deficiency, and this needs to be replaced starting now, and every day.
This is usually able to be corrected by lots and lots of rest, lots of water, food, and lots and lots of Calcium. What happens is they basically become very malnourished due to the egg-laying (both their bodies leeching nutrients from them to make the eggs, and then also the act of just laying the eggs exhausts them), along with the caring for babies, and of course the constant feeding of the babies for weeks and weeks. So this nutritional deficiency causes them to lose a lot of body weight, lose their feathers, and become extremely exhausted...
She needs to see an Avian Vet, as she would definitely benefit from a Calcium injection, among other things, and there may be something else going on with her, no one can know without examining her, taking cultures to rule-out an infection, etc. However, I understand that you're in a country with few vets, and this may not be possible...I can tell you from my 20+ years of Budgie-breeding experience that I've seen this a few times with female breeders...Budgies are hardy little birds, but they are little, and unfortunately they can often have massive clutches (I've had clutches of up to 13 fertile eggs before, too much for them to lay and care for) and this happens a lot of the time, so I'm guessing that this is the issue...So the first thing you need to do is put her in her own cage ASAP, with her own toys, her own ample amounts of food and water, Cuttlebone, Mineral Block, etc. And if she's feeding babies right now in the nest box, you're going to have to either try to get another pair to feed them, or feed them yourself, because she can't handle it right now, obviously. She needs lots of nutrition, water, Calcium, and rest by herself. It takes time, but they typically will start to recover within a couple of weeks if they are not too-far gone, but she absolutely cannot feed anymore babies, nor be bred again...
