I am an MD, and I second the advise about a beta-blocker. It's not uncommon for professional performers to have true "stage fright", and a number of them do indeed take a beta-blocker. This is not a sedative medication, but rather it has the effect of slowing heart rate, thus decreasing the breathing difficulty and clammy hands.
Of course, internet chat boards are not the place for medical advice, but I would at least discuss it with your physician to see if it would be appropriate in your specific case.
Other ideas, beyond looking very carefully at the routes and choosing the least of the bad choices: Change your seat away from the "edge" side to the middle of the road side, keep your back to the edge at all times and watch the scenery opposite the edge side. Play some music, perhaps with headphones on. Anything to distract your senses, as in most cases the difficult part of these roads lasts no more than 15 to 30 minutes.
