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What kind of cough does he have? Is it productive/ has phlegm? Or dry? Is there fever
or any other symptoms?
You will have to take him to his pediatrician
again ,for an examination and a new prescription.
Its common for children to have respiratory tract
infections, espcially at the change of weather.
If the problem is recurrent , you can try Homeopathy
Meanwhile , give him plenty of warm fluids, rest and steam-inhalation.