You're under the care of a doctor and he's going to take them out as a precaution. He'll send them off to a lab to test them for melanoma or anything like it. If it is something, at this stage it sound like it will be very treatable. It is probably nothing, though. Don't worry until you know more.
If you are concerned about skin cancer, stop tanning. They have good fake-and-bake tanners out there that look real and don't cause cancer.