Arthur,
My wife has written a lot on this forum (ntbowen) about our son who is 3.5 and has ticks. He also has cockroach, dust mite, and corn allergies along with wheat/dairy sensitivity. He also HAD asthma. I say had because when we (mostly my wife) removed the corn, wheat, dairy and took all precautions possible against dust mites his coughing attacks went away along with his asthma attacks (so far). In the past, every minor illness became an asthma attack that was treated with a nebulizer. For the past two winters he was on steroids to prevent the attacks. This winter, several illnesses, no asthma coughs, no steroids.
I guess what I am saying is that you might want to address dust/dust mites/food allergies as well.
Good luck
Chuck