Hi deep_sleep,
I'm not sure if you're still dealing with this but I had a blocked tear duct a couple months ago.
I did the exercise in this video only once and 30 minutes later something huge came out of my nose and my tear duct was
open again.
I can't guarantee that it will work but it's only a 3 minute exercise so it's worth trying in my opinion:
https://youtu.be/pleb21inrm8I actually just did it again because I had a cold and my tear duct is closed again. We'll see if it works, once more.