T.,
It sounds like allergy induced asthma. My daughter was diagnosed three years ago (she is 7 now). Her dr out her on allergy meds, zyrtec(oral) and flonase (nose spray) as well as asthma control inhaller, and a resuce inhaler. I check pollen levels everyday, as well as air quality (one of her triggers is smog), As soon as she shows any signs of allergies I put her on her meds. We have been very lucky that we have it well under control and she can do everything outside that she wants to, though we do have to watch her if we are out in very cold weather.
I would make an appointment with your childs doctor to check for allergy induced asthma.
Good luck
Amanda