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In acute viral illnesses , the coughing may be due to the dripping of mucus to the back of the throat or mucus in the passages of the lung itself or sometimes hyperactivity or inflammation of the airways. Since he has a runny nose, it is likely that the secretions are going back into his throat and contributing to his cough.This would be treated by: propping him up if possible when he is lying down, use of topical nasal decongestants such as otrivine for 3 to 4 days, oral decongestants. You can also consider the use of children vapour rubs which would also help to clear his nose. A cough suppressant can be used along with the decongestants.
If he has a wet cough then a mucolytic
with a beta agonist medication is indicated- these medications can often be combined into one syrup.
So - prop up, childrens vapour rub, oral and topical decongestant, keep environment warm (if he is cold
he will cough more), cough suppressant.
If wet, mucolytic can be used.
Hope this helps