Good advice. I'll also add that if you're in a temperate region, heaters are kicking on this time of year in a lot of places, blowing around a lot of dust and the like. Kills my allergies every year. If it just started, that's another thing to look at.
Also keep your eye out for squinting, excessive pawing/rubbing, or goopy yellowish, greenish, and/or stinky discharge. My poodle had a couple rounds of eye infections when he was younger, and they started with excess tearing. Just get back to the vet if it seems to be getting worse or causing significant discomfort. Hope you find out the cause soon!
Also keep your eye out for squinting, excessive pawing/rubbing, or goopy yellowish, greenish, and/or stinky discharge. My poodle had a couple rounds of eye infections when he was younger, and they started with excess tearing. Just get back to the vet if it seems to be getting worse or causing significant discomfort. Hope you find out the cause soon!