Well, you could give him tylenol cold or just stick it out. Colds shouldn't last more than 10 days, so if it does I would take him to the doctor.
The doctor probably told you not to give him any water until at least 6 months, because that can cause water intoxication in children under one. Especially in the first 9 months. Too much water dilutes a baby's normal sodium levels and can lead to seizures, coma, brain damage and death.