What you're Green Cheek is going through is completely normal, as the other members have already stated above...It's a combination of hormones and just being a Green Cheek Conure, as FlBoy already mentioned, Green Cheeks are very stubborn and will not back down, but the last thing you ever want to do is to "Punish" him in any way or give any "Negative Reinforcement", because it just doesn't work. Yelling, scolding, or any type of physical punishment when he bites, such as the very common and terrible advice that people give of "Tapping/Flicking him on the beak", which is the worst thing you could do.
***Have you actually had your two Green Cheeks DNA-tested for gender? If not, I highly advise that you do, so that you'll know for certain what both of their genders are. If either or both of them are females then you need to be prepared for egg-laying (infertile eggs if they aren't mating), and the other issue that you might be dealing with is if they are of the opposite sex then not only may you end-up with fertile eggs, but that can make their hormones all that much worse, especially male Green Cheeks, which sounds to me like Tequila's gender from what you're describing, though you never know until you get them DNA-tested...
****BIG QUESTION FOR YOU: Do your birds have access to any small, dark places that they can get inside of or underneath? This can be either inside of their cages in the form of any types of birdy Beds/Triangle Beds, Tents, any of the "Happy Huts/Snuggle Huts", any Hammocks, or any type of Boxes, such as cardboard boxes or similar...And this can also include your birds having access to small, dark places when they are OUTSIDE of their cages, such as being allowed to go underneath of furniture, going behind pillows, and getting inside of drawers/cabinets and any Boxes that are laying around. This also includes them having anything in the bottom of their cages that resembles or that could be used as Nesting Materials, such as any types of pet/animal "Bedding", Wood Chips, Shredded Paper, etc.
***I have personally seen/experienced my own Male Green Cheek Conure, Bowie, suddnely transform into a little Psychopathic Monster in a matter of minutes due to his hormones being turned-on and out of control due to him going underneath my couch...I brought Bowie home as a hand-raised baby Green Cheek when he was 13 weeks-old, and he will be 3 years-old this May. He's the sweetest, most-loving little parrot in the world, and he could not be any more-closely bonded to me than he is. (I am single and live alone currently, so it's just me and the birds/dogs/Bearded Dragon)...I love all of my family very, very much, more than anything in the entire world, as they truly are my family...That being said, my relationship with Bowie is special, for whatever reason Bowie is like my own little child. And besides him doing the typical, every-day nipping/beakiness that most-all Green Cheeks do, especially males, Bowie has not EVER actually bitten me...EXCEPT FOR THAT ONE DAY. And it was sudden, unexpected, and actually scary to me because as quickly as he turned into a little monster, he also came right out of the hormonal "trance" that he went into, and went right back to being my little Bowie baby...
Long story short, I couldn't find him one day, and he wasn't flying to me when I called him, which is really unusual. My Quaker Parrot was pacing back and forth on the top of the back of the couch constantly, and I knew something was really wrong. I actually thought that Bowie had either gotten outside somehow and had flown-off, or more-likely he was dead in the house somewhere because he wasn't coming to me, responding to me, making any noise at all...So i got a flashlight and started looking frantically for him all over the house, and then I found him underneath the couch, which has maybe an inch or two max of space underneath it. He was in a sort of "trance' where he had gathered-up some pieces of paper and other stuff he had found under the couch and was sitting in the middle of it like it was a "nest". He was making this constant little "chirping" kind of noise, and was totally ignoring me and what I was saying to him, even though he was looking right at me...He wouldn't come out on his own, so I got a yardstick and swept him out from underneath the couch towards me, and he literally "charged" at me, came running right at me and latched-onto the skin on my hand between my thumb and my index-finger, and he wouldn't let go. I was bleeding and he just wouldn't let go, and I had to finally pry his beak off of my hand, and he then landed back on the floor and ran full-steam right back under the couch!
I cleaned my hand up and then looked under the couch again and there he was...So I again took the yardstick and went to sweep him out from under the couch, but before I could he came running full-steam out from under the couch on his own and this time he attached to the skin on the top of my foot! I was trying not to scream/yell at him, and honestly I was more concerned as to why he was doing this out of nowhere than the actual pain (this happened about a year or so ago, so when he was between 1 and a half to 2 years-old)...I pried his beak off of the top of my foot and grabbed him this time so he couldn't go back under the couch, and I just took him right to his cage, put him inside, and left him in there by himself in the living room for about half an hour to cool-down...And when I came back to his cage about 30 minutes later and opened his cage up, he came flying right to me and was his normal, loving self...And it's never happened again because I've made sure that he can no longer get underneath of any furniture or into any other small, dark places.
Since your bird started doing this out of nowhere and hasn't stopped doing it since he started, my suspicion would be that he has access to some kind of small, dark place that he can get into or underneath on a regular basis. If it's not that, then there is another reason that his hormones have been constantly in overdrive like they have been, and it could be the other Green Cheek being the opposite sex...Do your Green Cheeks both live in the same cage? This is another important factor that could be contributing to his constant hormonal drive. If he doesn't have any type of small, dark place inside of his cage or that he has regular access to outside of his cage, but you do keep your Green Cheeks in the same cage, then the next thing to try would be to separate them both into their own cage or their own "territory", and give that a good couple of weeks to see if that produces any positive changes. They can have their individual cages in the same room and near each other so they can still see each other and talk to each other, since I guess they get along well (or used to until he started becoming aggressive), but they need to each have their own territory with their own toys, food/water dishes, etc. This could do wonders to calm his hormones.
All Green Cheeks and all parrots for that matter are going to go through puberty and have hormonal periods, that's completely normal...However, what you're describing that he is going through and will not snap out of is a sudden and now constant hormonal aggression, and when tht happens there is usually a "Trigger" that is causing it to be continuous, and finding this "Trigger" and removing it is a process if there isn't anything obvious like a Happy/Snuggle Hut, Tent, Bed, or Box inside of his cage, or if he isn't sharing his cage with another Green Cheek...
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