I realize your request is a little old. I'm new here, and I felt I needed to share with you. My daughter has asthma and allergies too.
I agree with the moms who told you about having your son tested for allergies. Seems like they go hand-in-hand.
Before we had my daughter tested for the two, she would clear her throat and cough, a lot. I would just treat her with some OTC meds. It wasn't until a doctor heard her cough, that they took it seriously. We were referred to a allergy/asthma specialist. We found out she was only breathing at about 50% capacity... and has a pretty moderately allergy to cats, and seasonal outdoors things.
Since we got her on her meds, rarely does she have episodes.
She's taking Pulmicort, (an inhaler), Nasacort, (nasal spray), and a generic form of Benadryl. She was on a Rx before the Benadryl, but she woke up every morning and her face, eyes and lips were swollen. She has her Albuterol rescue inhaler and her nebulizer and a good ol steroid stand-by in case things get real bad. Oh, did I mention she's also taking allergy shots? Right now she's at every two weeks. She's been taking them for just over two years. She got about another three to four years to go.
Good luck with your son. Asthma sure does keep you on your toes! If you have any questions, let me know! ls