I'm not sure the AC is doing you any favors, my understanding is it actually removes moisture from the air. I think you are on the right track with the humidifier idea. Not sure why you can't find one in stores, maybe it's a seasonal thing?
I have the same problem, although it's not as severe as yours seems to be. I try to keep my nasal passages moist with distilled water (do NOT use plain tap water) or the nasal spray like you're using. I live in the Pacific Northwest, so it's not as big of a struggle for me. It's really important to keep everything moist, that helps a lot with keeping germs out of your nose.
Let us know if your doctor has any advice other than the spray and the humidifier!