Oh my goodness I'm so terribly sorry that yall are going through this right now. I agree with
@Shezbug that putting him outside is probably your best option.
This is exactly what I was afraid of happening with me when after 17 years of having various parrots(usually only 1 at a time) I out of the blue developed terrible allergies to my Linnie. For months I'd had a deep hacking cough that just wouldn't go away and I'd wake up literally every night multiple times coughing so hard I was genuinely afraid a few times that I'd be unable to breath it was quite scary. I also felt so incredibly worn down and just so miserable no matter what I did. I tested myself for covid so many times and always came back negative but I admit I'm a stubborn person and just figured eventually it would go away and I'd just suffer until it did never ever even thinking it could be Bosco.
Then fast forward to when I had to take him to work to board while I got my apt sprayed for ants and that night I got home from work and was airing my bedroom out with the fan going and door open(which normally I could never do because my dog was very prey driven and aggressive towards him so my bedroom door was always shut for Bosco's safety.
So I did notice sorta offhandly that that night I wasn't coughing nearly as much as I was reading in bed but didn't think much beyond it just sorta in the back of my mind. Then for the first time in months I was able to sleep through the night only waking up to cough once which was a massive difference but then it dawned on me that the only thing that was different is that Bosco wasn't in there with me.
So to be as sure as I could that him being gone was what was making a difference I spent the next day after work deep cleaning and disinfecting my room and moved his cage into the living room,laundered all my bedding(which I did every week but he was always in my room before) scrubbed down the walls,vacuumed the carpets ect and the difference was night and day I was hardly coughing at all during the day and was sleeping all the way through the night and it was like a weight had lifted off my chest. I didn't realize just how badly I felt until I didn't anymore if that makes sense it was completely night and day and it was painfully obvious that Bosco was the problem.
Because after that first day or so my symptoms greatly lessened and only flared up when I had to take care of him at work and I'd instantly start coughing when I had to be around him for even just a few mins.
So as much as it absolutely broke my heart I had to make the extremely painful and difficult choice to rehome him and end my life with parrots. I cried myself to sleep so many times after making that choice but I knew that for my health and happiness it was something I had to do because in this small apt there was no where I could move Bosco to that was safe enough from my dog or far enough away from my bedroom to make a difference. I was so incredibly lucky that within a week of him being gone that all my symptoms went away and I seem to have come out from this unscathed and I'm eternally grateful for that.
I absolutely feel for yall and I'm so incredibly sorry that your all in this situation. It's such a tragedy that our beloved birds can effect us this way. I really hope that if he can be moved into an outside aviary that she'll be feeling better and able to make a recovery.
It's strange as he has come for a head scratch now and Rachel is not coughing at all, so it isn't feeling like he is causing the trouble. Its just pure fun and enjoyment around him, yet wanting to protect yourself and survive due to what the hospital are saying! We are hoping for some miracle that all this is wrong and he can stay.... 
