Would it not be covered, in some part, by your 5th amendment in some cases?
If the government is asking the question, you have constitutional rights. If its not the government (even if its being asked for them), a different set of rules applies. It depends on the tricksy legal system, to decide if your doctor (in this case) is acting as an agent of the government in this instance. (not a lawyer, just my private opinion)
They can't make something a crime after the fact. (Ex post facto)
They aren't supposed to be able to do this, but they have found ways to do what has the same effect. In the case of the domestic violence thing, they did it by using the specific language of the law to get their desired intent.
The way it was written used the potential punishment as the standard. No matter what the sentence actually was. Yes, you did plead guilty to a crime. BUT at the time, the penalty for that crime did not make you a prohibited person. New law, and now that old conviction NOW makes you a prohibited person. That may not be ex post facto by definition, but it certainly is, by effect!
here's another point to consider, already sort of mentioned, doctors take notes, about everything about you, when they see you. These get into the records. Your general appearance (neat, unkempt, etc), and your state of mind (calm, agitated, etc.) are part of that.
If you get in their face about "stupid invasion of privacy" questions, you might wind up with a note saying "Patient became agitated when asked routine questions"...implying you are mentally unstable.
The risk we face currently, is that despite any, and all promises and despite even laws intended to protect us, private personal information is going to wind up available to agenda driven bureaucrats with the stroke of a pen, and some clicking on the keyboard.