Answer: , Hi dear.... This is might a case of blocked tear duct , its very common in new borns and subsides with time.In the nasal corner of eyes everyone have a tear duct that allows the natural tears coating the surface of our eyes to drain. A blocked tear duct may occur in your infant, and this will prevent the tears from draining normally. Instead, the tears will pool in your child’s eyes and run down her cheeks.A blocked tear duct in an infant will often resolve without treatment within the first year. However, your doctor may recommend massaging the tear duct to help relieve the blockage. You massage the corner of her eye for 1 min 2-3 times a day. If the problem persists and lead to some redness and infection contact a doctor.