Have you tried nasolacrimal duct massage to open the blocked duct? Here's a description from BabyMD:
The tear duct should be massaged by placing your little finger in the corner of your child's eye in the same place that you felt the knot in the corner of your eye. With medium pressure, press on this area in a downward motion about 10 times on each side. Remember you are trying to milk the tears along the duct, even though this area is only about 1/4 to 1/2 an inch long in your child.
(Google something like "blocked tear duct infant massage" for a diagram and other info.)
My son had a blocked duct without an infection. We massaged it a couple of times a day with light pressure (not medium - he was teeny). It cleared up and never came back. Of course, if he has a bacterial infection as well as a blocked duct, massage isn't going to be and enough and he'll need antibiotics.
Congratulations on your little one, and I hope he is feeling better soon!