Go see a pediatric ophthalmologist.
My family has a history of bad vision and eye problems so we took our 6 month old in for a check up with a pediatric ophthalmologist. His vision is fine, but we did find out he has a tear duct obstruction or ‘leaky eye’ it’s constantly wet which allows for bacteria to grow. It usually remedies itself, and you can massage the duct to help with the flow, but if not there is a tear duct probing procedure the doctor can do.
I did a quick Google to see if I could find more specific info. See link below:
http://eugeneeyecare.com/conditions/Overflow_Tearing_and_...