P.M.
What an agonizing situation for both of you. As a person with life-long lung problems, I find that house dust really aggravates my wheezing and coughing, especially when I'm fighting off a cold or flu bug. I have to periodically wash all my blankets and take my sofa pillows and cushions outside and beat the @#!% out of them. It's amazing how much dust will rise when I do this (I wear a dust mask during this process, and put on clean clothes after). So if there is any chance of dust lurking where you haven't thought of it before, go after it.
The viruses circulating this year have been unusually hard on lots of people, including some who don't usually develop lung problems. I caught both flu bugs this winter and had to increase my inhaled steroids for several weeks. This medication does reduce reactivity to irritants from all sorts of sources and I was exceedingly grateful I had them. Steroids administered for an acute illness, under a good doctor's supervision, probably won't be needed for very long. Long term use of large doses can have undesirable side effects, but it is potentially very helpful in the short term (or at the relatively small doses in my inhaler).
If you are not confident in your doctor's judgement, you might do well to take your daughter for a second opinion. I wish you all well.