I hate to be the one to tell you this, but no, this is not a violation of your rights. You didn't have to show her your scar - you could have refused. Likewise, she can ask.
There is little to know written law in Virginia as to what is and what is not permissible in the work place. Clearly, discrimination is not permitted. Neither is sexual harassment - but the rest is just a gray area.
I know it sounded like an odd request - and it was, but it is not actionable in the legal sense.