Who do you go to to get a medical certificate for stuttering?

Who do you go to to get a medical certificate for stuttering? I have spoken exams, i.e. vivas, coming up and would like to get a medical certificate for stuttering. Also I'd like it to be acceptable for the IELTS exam I have to apply for. Caveat: I'm from outside USA. Should I go to a general physician, psychiatrist, psychologist or speech therapist? When I searched up "speech therapists in _ city," all I got was recommendations for psychologists. I am so confused. Can someone other than a doctor give me a certificate?