I've met a few medical students / doctors who had issues with being squeamish around blood, wounds, or dead people. For some it was a real challenge, but they managed to get through it. For some people, the gross anatomy course was very anxiety provoking, having to dissect a human cadaver. I've talked to some people who met with a therapist and did exposure therapy to deal with their anxiety / phobias, and they found this helpful. It's not easy confronting phobias, but if you are motivated and have a therapist experienced in anxiety disorders / phobias and cognitive behavior therapy, most people can manage.

The toughest areas were the gross anatomy course and the surgery rotation. Some students were able to do exposure thearpy in advance to deal with being in the operating room. If you talk to someone in medical school early on, you can hopefully find someone sensitive to the issue who can help you get exposed to whatever makes you anxious in a reasonable way.

Most medical schools won't have you drawing blood from people or inserting IV's right away, but probably in the first or second year you will get exposed to that. The gross anatomy course is typically a first year course.

There is some research to suggest that blood phobias are slightly different from other phobias in the type of biological response people have who are truly blood phobic. If you have a serious blood phobia (pass out at the sight of blood), then you may find it much more challenging than someone who just feels anxious and uneasy at the sight of blood. With most phobias people don't pass out, but some people with blood phobias do faint.