Hi John. My goodness you are having a rough time! I am so sorry you have been so ill and that you also had the heartbreak of losing one of your beautiful little parrotlets. I sincerely hope things get back on track for you all - it sure sounds like you are dedicated to the cause!
I am pretty sure I am allergic to Kiwi although I have never been diagnosed. I say that because my ears get itchy when she sits on my shoulder for too long and I get little red hives if she scratches my skin. I have allergies to pretty much everything outside (pollen from everything) so during the spring, I find I am even more sensitive to her (the hives are itchier longer, for example). I also have asthma so allergies are definitely a trigger. Fun…
I have never done any type of intervention on Kiwi. Instead, I recently bought a Dyson stick vacuum and wow - does it suck up dirt and dust! It was a bit shocking to me to see how my current central vac wasn’t doing the job. There is definitely a noticeable change to my allergy symptoms and incidences of asthma. I use the vac everyday (sometimes a few times a day) because it is so light and easy to maneuver. It is also cordless - you just pop it off the charger and away you go. I vac the furniture around her cage too.
I am also looking into purchasing a HEPA air cleaner. I had one many years ago when I met my husband and had cats. He was very allergic (suffered asthma when he was around them) and as I would never have given them up, I worked hard to find solutions just like you are. The HEPA filter was also a game changer and I am sure the technology now is even better. I also vacuumed every day and particularly before he came over. He would typically only get itchy eyes and sniffles if they came close to him (which they always did - haha!) but it was rare that he would get asthma.
Another thing that helps me alot is a humidifier. Making sure your home has 45-55 percent humidity will help your health, your parrotlet’s health and your home in general (hard wood floors, wood furniture, etc). I breathe much better when the house is properly humidified - like, noticeably different. My sinuses too don’t get dry and sensitive, which can ease allergy symptoms.
As I already take Reactine in the spring for seasonal allergies, I notice the relief from the itchy hives during that time (but my ears always itch - there is more going on there, lucky me). I am not a doctor nor a pharmacist but you could talk to those professionals if you think that could help.
I think it is great that you are trying so hard to find solutions for your little guy. My little dog, Paris, passed away last December and I always thought I was allergic to her a bit (she was a major shedder). I wish I had had this vacuum when she was with me. Breathing difficulties are scary and absolutely need to be addressed so I hope some of these ideas can help you. Keep us posted!