Welcome to YorkieTalk. If your pup's eyes are making the sides of his face wet, I would take him to the vet. Eyes should not water that much.
Also, water is not the ideal thing to use to rinse eyes. Plain sterile saline made for eyes would be better. Stay away from fancy eye drops or medicated eye drops. These can make matters worse.
__________________ Kristin, Max and Teddy  |