Hi Nora,
I think you are amazing! Pulling up the carpet yourself AND laying tile. When you go for it, you really go for it! I am so happy that with the changes you are making, Katlynn is doing well. The carpet removal is going to make a difference. With everything you do, you will start to see improvement. It takes time. She didn't get like this overnight. But if you stick with making changes, you will start to see less exacerbations and ultimately less antibiotics. And hopefully lung function will start to go up too.
I liked your idea of putting filters in the vents. That's one I might do too. A few more suggestions you can try if you like. Think about an air filter. If not for the house, then for her bedroom. Ask the doctor about Claritin and Singulair (as mentioned by others). They both help so much. If her doctor approves, Costco has generic Claritin under the name Allerclear. Nasal Rinses are great to clear the sinuses, so mucus doesn't drip down into her chest. It's also probably better to clean when she's not around or have her stay in her room if it's possible. Mostly the less irritants her lungs are exposed to, the better she will be. Also if you use other products with a lot of fragrance like wearing perfume, or very fragrant shampoos, it would be better if you and other family members didn't wear them around her.
I still don't want to overwhelm you with a million things. I think what you are doing is great. Please keep us informed with her Katlynn's progress.