Only the vet can diagnose, but yes, they definitely can have a blocked tear duct, and the rusult is exactly as you’ve described. If your vet might be open today, it’s possibly worth a phone call to ask if a regular appointment is available, and if not, to go ahead and schedule an appointment for later in the week during normal hours. That should spare you any emergency charges which don’t sound necessary from the lack of other problems.
I only say this because my Spockie had a blocked tear duct that made him weep clear tears every few months or so. No other problems, and once the vet diagnosed him (she used this cool blue light to look into his eye) she prescribed an ointment that I used. It was a dab of goo in the corner of his eye that melted with his body heat, flushing the eye and clearing the duct. It always worked after just a day or so, I kept it in the house and from then on reapplied it as needed with a fresh tube on occasion. So if that’s all it is, I can reassure you on that point.
My only concern is if it’s more than that. You’re watching closely, and with normal behavior, eating, pooping, no nose discharge, no respiratory issues and no meatloaf position or grinding teeth, I’d guess that you’re safe to make an appt. for Wednesday. I change my mind very fast on that, however, if ANY other symptoms show up.