For 3 mo, left eye has been producing one tear at a time out of outer corner of eye. remainder of eye and other eye unaffected. no itching/redness. ??

See an doctor : This is a rather specific complaint and would best be evaluated by an ophthalmologist

Possibly : Possibly you have asymmetrical tear duct or mild swelling of this canal between nose and eye on left eye after mild cold. To be sure you need to see a doctor. But you can try to help yourself with compress of warm camomile tea for left eye 2 times a day for week or 2.