Re: Moving to Arizona
While the Arizona deserts used to be good for asthma and allergies, this is not necessarily the case anymore. The warm dry weather in the desert can help but we now have so many non-native trees and plants that Tucson has one of the highest pollen levels in the country! Allergies and asthma are very common here. I know people who didn't even get asthma until they moved here and others whose asthma got worse.
The problem is that non-native plants are pollinated by the wind while most native plants are pollinated by animals and insects. Since it's very dry here and often windy, pollen from non-native plants easily becomes airborne.
When I moved from New York to Ft Lauderdale in the mid-70s, my asthma improved, probably from the warmth. However, my nasal allergies got worse, maybe from the mold.
Since I moved to Tucson 11 years ago after 17 years in Boston, my asthma has gotten worse. I only used to need an albuterol inhaler during exercise and the change of seasons. After I moved here it got to the point where I was using it more than 4 times a day and still wheezing. Finally I had to go on inhaled steroids plus Singulair tablets. Fortunately, I am well controlled on a small dose.
So it's hard to say whether moving to Arizona will help. Your daughter should at the least spend a good amount of time here to see how she feels. Keep in mind though that it can take 2 years in a new place before you get sensitized to the local environment.
She may still need medication but maybe even with the increased pollen she'll get enough relief from the warmth and dryness that overall she feels better.
I wish there was an easy answer. For me, even though I'm taking more medicine now, I do think the warm dry weather is better. I also used to have terrible allergies from heating systems and that's not much of a problem here.