It really sounds like a blocked tear duct. Sometimes babies get these ducts blocked and one simple thing you can try is to gently massage the area between the top of the nose and the corner of the eye. Make sure you don't push too hard. Gently massage in circular motions. You can also do this massage with a warm wash cloth. Try this method several times a day and it should clear right up within a few days. If it doesn't go away after a week, best to go seek medical advice/
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