One more thing

In the worst case you can not prove his negligence, you still have a battery cause of action.

To prove the negligence case, you need an expert to testify that (1) this bleeding situation does not normally happen without the doctor's negligence. This will be your biggest hurdle and where you need expert opinions. (2) the harmful instrument is within the exclusive control of the doctor. This is a no-brainer since he was the one, maybe some nurses to operate on you (so the nurses may be co-defendants). You don't need to eliminate other possible causes, such as your super-sensitivity, for example. All you need to do is to prove that the doctor's conduct is more likely than not the cause of your injury (>51%).