It is important to consult a doctor before giving any medication to a baby, especially for a baby as young as 3 months old. Using a nasal aspirator to remove mucus from the baby's nose can help alleviate coughing. In case of fever, it is safe to give Tylenol, but Advil should only be used if Tylenol is ineffective. If the baby has a fever for more than 72 hours, has greenish nasal secretions, or if cold symptoms persist for more than 7 days, it is recommended to seek medical advice.