Finding a mental health professional is kind of subjective, so recommendations are not necessarily helpful. (Do pay attention to negative ratings though.) Even the most qualified ones can't help you if you don't "click" with them, so you may have to shop around a little. Don't be shy about switching if a psychiatrist or therapist isn't working for you; they're used to it.

Lastly, and this is my opinion only, if you have a teaching hospital nearby (e.g. at your nearest major university) with mental health services, you probably have a better chance of not getting a psychiatrist/therapist that's incompetent. No guarantees but a better chance. (Depending on your confidence in this thesis, it may even be worth paying out of pocket if they're not in your insurance network. After all, what is your sanity worth?)

Good luck.