Your feelings and reaction sound severe enough that I would recommend a therapist rather than a coach. While coaches can be very helpful with career issues and many can help with low-level anxiety in that conext, what you describe seems well beyond the training of a career coach.
Find a good therapist to help you develop strategies to address/manage your anxiety. I'd recommend a cognitive psychologist (behavioral psych) rather than a psychotherapist, but that's just my preference for something like this. Ask around or search this board for recommendations.
BTW, I'm intrigued by PP's advice to try beta blockers for the specific situation. Has anyone else done this? How did it feel?
Good luck, OP!