Odds favor that the asthma is secondary to allergies. Have you taken him to an allergist? If he gets his skin tested, maybe he can become desensitized with injections of the offending antigens.
Yes, we are on our second year of allergy shots. When they did the patch test on his back he reacted to all but 6 of the 40 allergens with which they pricked him. He is allergic to almost everything so its a long process.