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Since you have had an eye exam by an ophthalmologist already with no abnormality being detected with the tear ducts, then it is likely that you are having dry eyes. Ironically the first symptom of dry eyes is watering of the eyes which is a reflex , which occurs in response to the dry eyes.
It responds well to lubricating eye drops like preservative free Refresh tears , 1 drop 4 times a day.
I have already tried several types of eye drops for dry eyes, but they do nothing. I have had this problem for 4 years already.