Dog's tooth dilemma

My 16-year-old crossbreed dog has an infection of one of his cheek teeth.

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The infection is draining from a small area below his right eye. It responds to a course of antibiotics but then comes back. My vet has advised that the dog's best option is to remove the infected tooth. I am concerned about the anaesthetic in an old dog, and whether he will be in pain after the operation. Please advise.This is a common condition known as a malar abscess. It is caused by an infection of the upper fourth premolar (carnassial) too