Cough along with Cold most of the time is a  viral illness and it needs supportive care along with proper hydration. you can give steam inhalation which is very useful . cough needs to be treated with anti allergic and expectorant bronchodilators or antitussives medicine which should be given only after a proper evaluation by the doctor according to the type of cough. if fever is there paracetamol can be given to reduce the fever and the dose can be repeated after 6 hours again if required .

Viral infections are common in this season, some children getting sick with some complications. It's always better to see a paediatrician for a complete physical examination, especially the lungs, rather than self medication.