Hey vmo1. I also have exercise/allergy induced asthma. My allergist told me the best thing to do is not eat any fresh fruit/nuts/vegetables (that give me a mild reaction, itchy throat, etc) 2 hours before working out. I also have a bronchial dilator inhaler that I have to take 30min before working out. It's not an inhaler that is used for emergency treatment after an attack, but it definitely helps using it as a preventative measure. Also antihistamines help a ton too with hayfever that aggravates the condition.
I've heard that if you continue to have asthma attacks even if you're not completely constricted each time, that you can do damage to your lungs, so it's something you want to prevent.
And maybe you're running too fast and your cardiovascular system isn't used to it yet? Build up slowly, ensuring you have proper technique will help prevent your body from hurting too much (google running technique).
"Courage doesn't always roar. Sometimes itís the quiet voice at the end of the day saying, I will try again tomorrow."