Just wait. My son's tear duct didn't open up until 2 weeks after his 1st birthday. The ped told me that if it wasn't cleared up by 9 months that he should see a specialist. We decided to wait and keep working that eye. At his 12 month appt, it was a little better but still clogged. We made an appointment with the spclst but it wasn't until 2 months out. Then, magically, it was fine, so we cancelled the appt.
Every time he was in the high chair we took a warm wash cloth and gently massaged his lower lid from the OUTER eye area toward the tear duct. The area below the "puffy" part of the eye is where you want to concentrate working in an Upward and Inward motion. No need to put your baby through a surgery that could damage his tear duct (I've read good and bad stories about the procedure). This seemed to me like something that would clear up on its own, and it did.
Good luck.