Closed/blocked tear ducts!

My son was hospitalized at 6 weeks for conjunctivitis (pink eye) due to tears building up and creating bacteria. Doctor said many babies are born with this and that they open over time with massage and growth. Anyway, we were given a eye ointment to fight the infection and it went away fairly well. Now, at 11 weeks I'm noticing the same discharge that it started out with. I'm wondering if I just keep massaging it out and wiping gently with warm wet cloths if it'll go away. Has anyone experienced this before?

I have more ointment at my house however I flew back home for a couple weeks to see my family so I won't have access to it until next tuesday