I adopted a cat recently who is an absolute sweetheart ... is due to the nasolacrimal duct being plugged up. As for the swollen lip, it does not sound like a rodent ulcer since those are usually ...

Tartar buildup can rub on the inside of your cat’s lip, causing them to slobber ... Are the gums red, swollen, or even bleeding? Try a professional cleaning first, and then brush their teeth ...