Definitely take her to an allergy/asthma specialist.
Our family used to visit Dr. Kaplin when we lived in Corpus Christi. He taught us some basic living adjustments that have helped all our asthma (three of us used to suffer).
First, cover your matresses and pillows. I buy mine at Target. Make sure to use the plastic zipper kind. The others dont work.
Then, wash your linens and curtains in each bedroom at least once a week. (We cheat a little with the curtains, but we dont let it go too long because than we feel it)
While the curtains and sheets are in the wash, dust every inch of your walls, window sills and ceiling fans. Yes, it is alot of space to cover, but this is your/her breathing. Be sure to wear a dust mask and get behind every piece of hanging decor (pictures, etc.)
Do this especially where she sleeps, but if you can do the entire house. Everyone will feel better.
Vacuum your carpets often and if possible, replace with hardwood or other nonporous surface in the bedrooms.
The most difficult request that we follow if anyone has a cold or is feeling any triggers is to cut all dairy out of the diet. No milk, cheese, yogurt or butter. Instead use natural alternatives like soy milk or rice milk. Tofu cheese (cheddar is most like actual cheddar but none of these melt)
We also cut out chocolate and even now, we dont eat too much anymore whether we feel well or not.
I agree with the suggestion of getting rid of all chemicals used in your house. One of the best books I read in 2006 was "The Organic Housekeeper". We cut out all scented soaps as directed by Dr. Kaplin, but when I switched to all natural cleaning agents, the house felt fresher, the air (or maybe just my chest) was lighter and our grocery bill was slashed.
This is what I learned through years of being in doctor's care, hope you are able to help your daughter without having to keep her on steroid medications for too long.
M.