To whom do I turn for help resolving disputes over health insurance?

Depends. Depends on who the dispute is with. It is with a physician, i suggest talking to the practice manager. If it is with the insurance company, and a supervisor cannot help you, then you may need to go to the state insurance commissioner. We need more information on the nature of the problem.
Health Insurance. You are the owner of your insurance policy. You need to call your insurance company to resolve the problem. That is why they are there for.