I would get him tested for allergies-food and other things. We have a great allergy Dr. that we would highly recommend. His name is Dr. Tanna and there is also Dr. Haden and both are great. He sees adults and kids.
His contact info:
Dr. R. Tanna or Dr. Haden
1000 College Street
Fort Worth, Tx 76104
###-###-####
He does testing at Cook's hospital, and it is all done thru blood testing. We had our 2 year old tested and he is on medication. He also does a written report, which you will get a copy and he will send one to the pediatrician. He also gets an X-ray as well.
Our son had 2 sets of ear tubes and that has helped a lot. He's on Allertan and Nasonex and Singulair for asthma. He has an inhaler-albuterol also. He use to cough a whole lot, now it is very rare that he coughs.
I would try changing his diet and keeping a food log and see when he has the most trouble.
Hope this helps.