You came here seeking answers and you got them. That you don't like them doesn't make them the wrong answers.
Doctors and dentists are not obligated to render treatment except under very specific scenarios and a sore tooth is not one of them.
Feel free to files suit. There isn't anything stopping you and you're positive that you're correct. This is not to say that a lawyer can be compelled to take your case or that you are qualified to handle it yourself pro se...but you can.
So go, have fun! I'm sure you can find the appropriate court and they'll be some paperwork to fill out...but you've got this all under control.