Hi HarleyGirl,
I'm late to this and don't have much first person info to add that hasn't been already said. My mother has active asthma that sounds exactly like what's been discussed here right down to the list of meds you described. All I'm suffering from is living thru her long road to stabilization (it took years) and my own allergies to pretty much everything except food and meds.
Here's the short version. She really had to work at sterilizing her environment to stabilize her condition. It's a delicate balance she still diligently maintains. She's sensitive to fragrances and chemicals, pollens, grasses, trees, dust, and rabbits. Allergies to fragrances and chemicals is not treatable but the resulting symptom of asthma is.
I know I'm sounding like a downer right now when you really don't want to hear that but here's the thing. If your condition is aggravated by your chin, the best thing you can do for your recovery is to be honest with yourself. My mom is highly allergic to rabbits. I know this because we had two when I was a kid. Dad moved them from the family room to the back yard to help mom's allergies and they gradually built on her to the point where she couldn't be within 50 feet of them without some kind of asthmatic reaction. She couldn't breath in her own back yard. And she couldn't breath in her house when we came in after being out there! We had to give them away and we all cried. So like I said, you know if Squeaky is a problem for you and I sincerely hope you're right that he's not. If he's not, moving him to the garage will do nothing and is unnecessary.
Here's the fragrance problem for my mom. I mention this because chemical allergies are not mainstream and are not directly treatable and perfume is in everything these days and because I've encountered so many people who don't believe fragrance is a legitimate allergen (and because, in treating the resulting asthma, I was exposed to everything mentioned in this thread). Mom found the only way to treat her condition was total avoidance - of all allergy triggers. She uses a dehumidifier for the same reason Caiti does. There are no strongly scented household cleaners, detergents, dish soaps, hand soaps, deoderants, hairsprays, makeup, fabric softeners, air fresheners, paint, candles or any other kind of perfume in her home. She has no pets if you don't count my father. ;p She can't have fresh flowers in the house. She even reacts to peppermint candies and fragrant teas. She reacts to powders and aerosols. She can't have anything that puts ozone into the air so she's very careful to avoid machines that ionize the air. She gives every new appliance a trial period for this reason as well. Everything electronic ionizes the air around it to a certain extent, especially when new. She made a "clean room" of her bedroom and retreats to it when her asthma is really bad and she's tried everything else. No rugs in the bedroom and HEPA filters are her best friends. Her medications react with or negate cold remedies so she does everything she can to avoid getting sick. My family had to learn what we could use to stay in the house and had to continue to use those products when we moved out to be allowed back in. We stay vigilant for "Mom approved" products as the years change so we can continue to visit without causing her discomfort in her home. Her worst season is spring but every season has it's issues.
Me, I'm allergic to natural things like trees, grasses, mold, bee stings, birds and furry things. I sneeze alot in spring and fall. Lately I sneeze alot by the chin cage as my allergies build. I hope I don't have to take my own advice. I use a mask to clean all the cages and I have an air cleaner in my bedroom. I don't have an ion problem but avoid ionizers anyway. I don't enjoy perfume. It causes a metallic taste that stays with me and sometimes causes headaches and an ache in my chest. Mom tells me that's normal and I don't have her problem. Still, I have a mask on my desk at work. It helps some.
I hope fragrances aren't a problem for you, but if they are I hope my mentioning them helps you improve your peak flow. If you need a list of tolerable products my mother uses just let me know and I'll pm one to you. The internet is full of natural alternatives to household cleaners and such if you have the time to search for them, too. You asked about air filters and got good advice from others which I'm repeating - HEPA filters. Just make sure the filter you get can handle the size of the room you put it in. A little bigger is better than too small. It might be a good idea to get two, one for your bedroom and one for Squeaky. If you only get one, put it in your bedroom. I wish you luck with your tests and hope that you don't have the issue your doctor suspects.