Are physicist doctors

if they have studied for a doctorate degree (PhD), then yes. it is currently the highest level of education, and if studying for a doctorate, you do not learn as such, but produce your own theories.

if you are referring to a doctor as in doctors and nurses, then the answer may also be yes. radiologists who use machines like MRI scanners and X-Ray machines are using physics, and they have an MD

You may be confusing "physician" and "physicist". English not being my main language, I confused them at some moment. A physicist is an expert in physics. A physician is one who practices medicine, commonly called a "doctor".