It "normal" to have "white coat hypertension" if a doctor?

Yes it's "Normal": If you're asking if it's normal to have "white coat hypertension" if you are a doctor, then yes. Anyone, even a physician, can be stressed to be in a doctor's office. It is the stress that causes the "white coat hypertension". Everyone with newly diagnosed hypertension should get several blood pressure checks, like in a drugstore, or back at your doctor's office without seeing the doctor.

Does happen: You've taken the first step by acknowledging your difficulty. Psychologically the next step would be to identify your fears specifically and then confront them rationally careful to remove our tendency to catastrophize. Let your doctors know of your fear so they can help.