For an odd Arizona and asthma and allergies story: when my dad was about 6 or so, he had terrible allergies and asthma, and his doctor suggested they move out to Arizona. The whole family trucked out from Ohio to Tuscon; and this was while WWII gas rationing was still on so it was a big deal. They stayed for a couple years and then went back home. As an adult living in KY, Dad never had problems with allergies or asthma, except for one week. One spring break when me and my brother were teens we went out to Arizona, and Dad was sneezing and wheezing and miserable the whole time, worst when we were in the Tuscon area. Something was blooming out there in the desert that he hadn't experienced in decades and it didn't agree with him.

The native plants can cause trouble too, you never know what you might end up sensitive to.