I've only half been through this. For myself, when I was 9 mos old, my tear ducts were severely blocked. My mom took me to the opthalmologist and scheduled the surgery. One week before the procedure, my eye completely cleared up. Surgery avoided.
My son had a blocked duct until he was 9 mos old, too. Cleared up on its own. And my daughter had a really bad tear duct blockage from birth that would frequently get infected from when she was 6 to 9 mos old. After her 9 mo checkup, we got a new antibiotic eye drops, made the appointment with the eye doctor and prepared ourselves for surgery. Amazingly, one week before her appointment, her blockage cleared up! Cancelled the appt and haven't had a problem since.
In the end, it's up to you to make the call on when to make the call. there's no real harm in waiting a few more weeks, continuing the eye massages. Perhaps your dr can tell if there's an infection in there, too, causing the blockage to remain? Plus, going to the opthalmologist doesn't automatically mean surgery. Perhaps they can find another less-invasive alternative to start with before resorting to surgery?
Good luck!