Suggestion

First, you should directly and clearly request the detist to reimberse all the medical expenses related to the incident, either by calling or writing, probably both. Keep record of everything.

Second, if he refuses, or if you don't want to directly confront him, you probably should talk to an attorney, not necessarily for the purpose of litigation. A large part of lawyer's work is negociation and collection.

Of course, attorneys are expensive. Therefore, it all depends on how much your medical bill is. But you can call some attorneys anyway, tell them what your problem is and ask for their estimate for the service. Such initial discussion before you hire one should be free. Many times a phone call from an attorney could make someone willing to pay something.