Sarah,
Have you tried to go outside and just watch a good storm? It truly is exhilarating. The rain comes and cleans everything and the air becomes cool. I find storms to be very relaxing. Is your fear based on tornadoes, hail, or something dangerous within the storm, or just the rain? I am sure that Cognitive Behavioral Therapy would help, but it would also require a leap of faith on your part to go outside and stand in the rain because most likely your appointments won't always be on a rainy day. LOL. Meditation is also wonderful to help you relax.
Try to face your fear and see what happens. Don't go outside in a huge thunderstorm, but next time you get a little rain maybe go outside and sit in a chair on a porch and read a book. I think you will find it quit pleasant after the initial anxiety has passed.
Good luck,
OE