It sounds like a variation of Harry Harrison's "Arm of the Law". Title expands to "Automated Physician's Assistant, model 4000" - that's the robot assistant to a doctor; most of the story calls the robot Bob.
Clinic management has forced the robot as assistant on an unwilling doctor - so doctor does everything to get rid of the robot, until one fine day the robot really proves its worth...
Fact sheet.First published: Medgadget, 28 November 2008.
Download full text from publisher's site (need to click "Read More..." link at bottom of page & then scroll down to see this story)
Related: Robots in fiction.