4 days late, but I hope this reply reaches you. I'm a doctor that stutters, and yes it's difficult sometimes but in no way is it a reason not to be a doctor. When talking to patients, you get the words out eventually and you successfully convey your ideas. Do some people want you to rush? Yes, but that's human nature, you'll see that everywhere. But most people, your seniors and patients will be more than accommodating. As for the interviews, it's an absolute necessity to state that you stutter at he beginning of the interview. Because if you don't, they will take it as anxiety and that will hurt your application. However, once you tell them, most don't care about it that much and actually look past it.