A.E.
I would talk about it with your pediatrician. My eldest daughter was the same way, and after many doctors visits we finally went to see an allergist. They tested her for many differant types of allergies and did an xray to check and see if her adnoids might be enlarged. Turned out she had several allergies to outdoor pollens, slight allergies to differant pets and enlarged adnoids. They also found out that she had asthma, that is what the cough was, the trigger being the outdoor pollens. We started her on allergy medication, an inhaler and removed her adnoids. She was almost 4 when this all transpired. She is now almost 12 and is on no medications. She has pretty much outgrown her allergies and asthma. Sounds very similar to what she had. Talk to her doctor.