Sorry to hear this you need to learn to not give a fuck about what people think of your stutter. It is not your fault you stutter and you should not have to blame yourself for something that is out of your control. At the end of the day, I would not let stuttering stop you from trying to achieve your goals. If medical school is something you want to do, don't give it up because you stutter. The worse you can do is fail and your family is already rich so it would not matter