A cold and cough in a child for 2 days are usually due to a viral infection, and the cough may take a few days to settle. Give warm fluids, keep him well hydrated, use steam in the room, and keep his nose clear to ease breathing. Ensure proper rest, avoid cold exposure, and do not give multiple medicines on your own. If the cough is worsening, disturbing sleep, or not improving in a few days, consult a doctor to check the cause and guide proper care.