I have horrible "white coat syndrome" with anxiety acute enough that I faint and occasionally have mild seizures. This has happened throughout my entire life and, at times, was crippling enough that the anxiety spilled out into my daily life as I thought all the time about illness and doctors!
What helped me initially was anxiety medications, meditative therapy, and exercise.
I can highly recommend the One Medical Group for just being very non-medical about the whole doctor experience. There's a fee to join their group but if you use healthcare enough and truly fear going to the point where your health is at risk, it's totally worth it.
Best Doctors in NYC — One Medical Group