Coughs are usually caused by viruses and do not often require antibiotics.

Cough medicine is not recommended for children 4 years of age and younger, or for children 4 to 6 years of age unless advised by your doctor. Studies have consistently shown that cough medicines do not work in the 4-years-and-younger age group and have the potential for serious side effects. Cough medicines with narcotics—such as codeine—should not be used in children.

 

Source: American Academy of Pediatrics