E.C.
Both of my children had this, but our doctor had us massage the duct to help it open, which I think really does help. You should ask the doctor about this before doing it, but we were instructed to rub up the inner side of the nose (between the nose and the eye) toward the eye, to help unclog the duct. This makes the eye water a bit if done right.
I am sure different doctors have different approaches with this, so check first, but this did work for us.