If the child is asthmatic, frequent coughing ????? whether it???s dry or wet ??? can be a reaction to an asthma trigger such as cigarette smoke, dust mites or other irritants. ???If the cough is lingering, the asthma problem is not being treated,??? says Dr. Rauch. ???What you want to do is treat their asthma by discussing the best options with your pediatrician.???