The FDA has issued a public health advisory for parents and caregivers recommending that cough and cold medicines should not be used in children under 2 years of age. (The advisory applies only to over-the-counter medicines; however, the truth is that virtually all prescription cough and cold medicines for children are the same drugs that are in the over-the-counter medicines). They have not been shown to be effective in children this age, and can cause serious side effects and death in young children.
FDA Public Health Advisory: Nonprescription Cough and Cold Medicine Use in Children