I agree, it's probably a blocked tear duct. They are very common in newborns. I would have the doctor take a look at it just to be certain that there's no infection, but my guess would be no, since there's no redness.
My ds had a blocked duct in both eyes when was really little, but his left eye cleared up relatively quickly (probably within a month). The left eye however, continued to be puffy, and have a ton of discharge until he was about 5 mo. It ended up clearing up on it's own, and was very off and on (some days there was NO discharge or puffiness, and some days were terrible--he wouldn't be able to open his eye without a lot of cleaning it).
Sometimes massaging the inner eye works in opening the tear duct, when you're cleaning the discharge, but other times it just has to grow open on it's own.