A three year old child's eye has been constantly wateringwithout any irritation. should i go to a pediatrician or an eyedoctor first?

Tearing: If the only symptom is watering you can see the pediatrician. If he has pain in the eye or visual problems this could represent a more serious problem requiring a specialist. Is the eye red or itchy? Did the symptoms start suddenly with an injury or something getting in the eye. If in doubt start with your pediatrician.

Ophthalmologist: Tearing is due to either an over secretion of tears or a blockage in the tear drainage system. To diagnose this one would at least have to look at the eye under a microscope. As pediatricians do not have this equipment, you would be better served by going directly to an ophthalmologist.