I have no experience, and can only guess. ...tears. If your ducts are clear and free, not impacted, any additional tear production will drain into your nose or over your eyelids. I take it that you aren't 'tearing up' and have to dab at or wipe at your eyes, so that leaves me puzzled.
Is the discharge, when you can look at it in a tissue, any colour other than very slightly yellow? No pink stains, not greenish, not orange or deep yellow? So it's probably not sinus.
I hope you get some help here. Please be patient.