I'm asthmatic. I have two inhalers - one for daily use to manage my asthma and one for emergencies. I usually carry my emergency inhaler with me. Before races, I'll take a quick puff of the emergency inhaler to ward off any unwanted attacks. I've had no problems at all riding or racing.

As for the pollen, the best thing for that is a Neil Med sinus wash. I do that twice a day too to manage my allergies. It's a little weird at first, but works great. I also keep a bottle of Afrin in my cycling bag. A shot of that before the races helps keep my sinuses open to improve my breathing.