Dr. Greene's Answer
Kids can cough for many reasons. Colds are the most common, but they can also cough from croup, allergies, asthma, pertussis, inhaled irritants (smoke), inhaled foreign bodies, sinus infections, and tuberculosis — to name a few.
In general, the cough is a friend, not an enemy. It protects the lungs, clears secretions, helps to get rid of infections, and alerts us that the body is dealing with something.
If the cough is from a common cold, and it is interfering with sleeping or with drinking plenty of liquids, though, then trying to stop it may be worthwhile.
I do not recommend over the counter cough and cold remedies for children under 6. Carefully controlled studies have not been able to show any benefit – and in a small number of children they can have serious side effects. Yes, many children do get better when they take decongestants, antihistamines, and chemical suppressants for coughs and colds, but on average they get the same amount of relief from taking a placebo.
If the cough persists, get in touch with the doctor. Perhaps something more than a common cold is causing it.