My newborn has a very watery eye and a lot of gunk commin from tear duct, but no redness or sign of irritation, what should I do?

Massage. Many times just massaging just below the tear duct and using warm comresses and cleaning the area, will relieve the obstruction. However, if it continues, baby should see an opthomoligist. Somtimes they need to open the tear duct.
See pediatrician. Your child may have an unopened tear outflow duct (located in the tissue next to the nose). About 2% of newborns have this problem. Your pediatrician will instruct you on massaging and keeping this clean as many will spontaneously open. If the condition persists after about 6 months, see your pediatric ophthalmologist who has a way of opening it for good.
Common finding. The drainage pipe for tear fluid is relatively tiny at birth and clogs easily.If you roll the tip of your finger over the inside corner beneath the eye,rolling nose to eye,you can empty material in the tear sac beneath.Do this several times a day and the drainage may improve.If the lids become red call in, eye drops may be needed. Discuss the issue at your next visit.