hello... fellow tucson resident... (I've lived in AZ most of my life) just so you know the past few weeks have been much worse for pollen/anything airborne allergies than I can remember for a long time...

I'm definately allergic to my cats (have been allergic to just about everything as long as I can remember)... so I bathe them regularly with special cat shampoo (2-3 times a month)... one way to make bathing easier is to put a screen down in the tub, they tense up and their claws get stuck and they can't move nearly as much (A friend of mine uses this and swears it works wonders-I started with mine as kittens so they take it ok, but that's not always an option)
brush them frequently and try to vacuum often with a Hepa-filter vacuum. And they do make special air filters for A/C which filter out allergens/smoke etc that you can get at home depot or wherever for about 3 times the price of regular but worth it

And even if you can't keep them out of the bedroom, make sure they can't get on the sheets and especially the pillows

good luck!