Find a new vet. You don't flip a fearful dog over. That's a good way to cause fear agression and biting. Your vet has caused a behavior problem in your dog that could be dangerous. I'd fire him and make sure everyone I talked to within 100miles of him knew about it.
Step 2 work on bite inhibition and positive vet trips. Bite inhibition teaches the dog how hard they need to bite and when. Majority of it comes from their handling as a puppy but adults can be improved. Games that encourage biting of objects or gentle mouthing of arms with a release when you say so will help teach them how hard to grab and when to stop. Positive trips to the vet will help teach them that it's unnecessary to get defensive and bite in that situation. Find a good vet that will allow you to just drop by every so often and have them feed the dog treats and play with it. Then when you have an appointment start with some play, make sure the dog is not too wound up, and smoothly move in to the actual reason for the visit. With my defensive akita who had a bad vet experience (not the fault of the vet but of complications from spay surgery) we frequently drop by just to put her on the scale, give her a treat, and let everyone talk to her before going to the dog park. She's still bruised the vet twice but she hates being touched by people in the first place so being poked with needles in a place that bad things happened is plenty of reason for her to react. However because she has good bite inhibition, the vet has commented on it, she will not actually bite. She just taps arms or hands enough to leave a little red mark or pinched skin resulting in a bruise. She knows how and when to give warning without flying out of control because it's been taught to her every time we went anywhere and every game we played from the time she was a puppy. She also knows I will not force her back in to a bad situation like repeatedly seeing a bad vet.
