Fellow stutterer here, I had my US visa interview, I told them, before starting " I have a small thing to say, I block on a few words, I have a speech issue/I stutter" Then most of the interview was good ,and I was not nervous about stuttering. The same can be done in the US as the attitude is tolerant of, and accommodating for people with any sort of disabilities. Also there are many doctors who stutter who have made it in the US. Chin up and carry along. You could try for specialties that involve minimum speaking, or those that esp deal with persons with disabilities.