There are many causes of cough, some infectious or on an allergic basis and
some not, for example aspiration (into the lungs) of a foreign body. Allergy
is a reasonable consideration and can be present with cough the only “allergic” symptom. You might want to do a careful examination of his room, looking to the possibility of a new, allergic substance having been introduced. Also, cough (without wheeze) can sometimes be the only symptom of asthma.