No. OTC cough and cold medicines should not be given to children under age 4, according to the American Academy of Pediatrics (AAP). These medicines aren't safe for children this age and can have dangerous or even life-threatening side effects. There's also no evidence to show that these medicines are effective in children of any age.
If your baby is feverish and seems uncomfortable or unusually fussy, ask your doctor about giving him infant acetaminophen (if he's at least 3 months old) or ibuprofen (if he's at least 6 months old).