Am I in the wrong here? Does she have a case?

Well you didn't SEND him the picture. You also shouldn't have put it on Facebook. Had you sent that picture to him it would STILL be illegal, at least by US Standards, as you can't send pornographic images to a minor. Then again I don't think Facebook approves of nude pictures, you or anyone else, being put on their site. So yeah that would be breaking Facebooks TOS and could get your account suspended.