Cough along with Cold and fever most of the time is a  viral illness or allergic and it needs supportive care along with proper hydration needs to be maintained. you can give steam inhalation which may be useful . cough needs to be treated with medicine like anti allergic  expectorant bronchodilators antitussives or cough suppresents medicine which should be given only after a proper evaluation by the doctor according to the type of cough and need. In severe cough nebulisation can be given where medicine directly gets dilivered in the respiratory tract. Also if fever is there paracetamol can be given to reduce the fever and the dose is 15 mg/ kg body weight and can be repeated after 6 hours again if required . Home remedies like Tulsi & ginger mix in honey can be tried for soothing.

Nebulization for small baby at home is not advisable.