You could have a look at JAR FCL 3 on the JAA website for a full break down on the medical. You could have a look in the CAA website as well.
I have very mild asthmatic tendencies and I get through the Class 1 ok. I don't know what level of asthma you have so it's hard to give advice. If you are asthmatic then expect to have to go for a jog or something like that to see if your lung function is impaired in any way.