I'm an anxious person, and my husband is a therapist. One thing he does that isn't really therapy but helps me is to ask, "what's the worst that will happen?" when I'm stressed about something. For me, I love to sing but I get terrible performance anxiety--but I just love to perform! So part of me hates it but part of me loves it. He's asked me before performances, "What the worst thing that could happen?" and I have to admit, I might forget the lyrics, sing the wrong note, mess up in some way. "Okay, but would you still enjoy it even if that stuff happened?" And I have to admit, yes, I still would have fun, even if I forget the lyrics and have to start over. The embarrassment wouldn't kill me.
So maybe you could think about that. If your blood pressure is high, what's the worst thing that could happen? Ask yourself logically, use your rational brain, to help you figure out that everything is likely still going to be okay.
Also, one thing my voice teacher has asked me is where I feel my anxiety to determine what type of reaction I'm having--fight, flight, or freeze. I'm definitely a "flight" kind of reaction to high anxiety, where I want to run away--I will sometimes come up with excuses NOT to sing. And I get very shaky legs when I have to perform. They feel shaky, but they don't look shaky. It's like my body is getting ready to run from a predator, but I'm the predator, forcing my body to do something it doesn't want to.
It seems to me that some part of your stress response is getting screwy when you go to the doctor, like mine does before a performance. If you're like me, it might help to go on a run or brisk walk or something before going to the doctor, to get that excess adrenaline to wear off. If you're more of a fighter or one who freezes up, I'm guessing there are tips out there for those stress responses.