Non canalization of the  nasolacrimal duct is most important cause of watering since birth in addition to mild infection, mild infection will go with use of antibiotic eye drops. For for non canalization mother has to learn how to do lacrimal sac massage while lactating the child as described in text book, it gives hundred percent result in 1-2 months if done sincerely.It gives best results if done below 6 months old child. In late stage it not very successful & doctor has to probing under general anaesthesia,your child is already 3 yrs old ,how much probing will be successful ,I don't know but ophalmologist must try probing once in G A before taking any decision for major operation