Clean and massage. Your baby has a clogged tear duct. This is very common. First, you can wipe off the discharge with a clean washcloth 2-3 x/day. Then, you can massage the area between the nasal corner of the eye and the nose by rubbing it with a clean finger for 1 minute. You can massage the duct 4-6 times a day.
Yes. Use a warm water cotton ball to irrigate the eyes. Apply no pressure to the eyeball. Be very gentle. If it is both eyes, it could be an irritant like second hand smoke for example. It could be a lacrimal (tear duct) stenosis (narrowing). If there is nasal congestion, please have the ears checked because it could be more global such as viral or allergy. Check theses things with your doctor.