Natural vs meds. Cough, if not associated with fever, shortness of breath (sob) or chest pain, may be initially managed with "steam baths", vapor rub, or bee honey at home. Over the counter meds are indicated for kids over 4 years. Some I have found useful have guaifenicin in them (to loosen up phlegm) and dextromethorphan. If your child seems ill, has high fever or sob, make sure to take him to your pediatrician.
Cough. As mentioned, otc medications are not indicated and can be dangerous at this age. Also try salt water nose drops if there is congestion and position the child in an elevated position when sleeping.