In the couple I have had with blocked tear ducts it was because and infection caused swelling and as it healed the tiny little tear duct grows over, or seals shut.
In many cases this is permanent, but in a few the tear duct has reopened after a long period of time.
When I was using false tears , and or eye drops some would always get in the fur around the eye, so it always looked matted, worn or ruffled. Then they tend to rub it as it itches, so it does get scuffed up around the eye. I can almost see how bad it is by the state of the fur around the eye. If the fur feels damp/cool and gooey it's infection, if it feels hard and crusty with no discolouration it's usually the dried up eye drops.
I was also rubbing their faces against mine to tell for wetness, but I wouldn't recommend it. An infection and spread to your eyes. Try using the underside of your arm, around the wrist, your not likely to rub that part against your own face, and it's pretty sensitive.