Im also seeing a psychiatrist and I can confirm that its VERY essential to see one as a person with stutter. We all definitely have abnormality in our brain that causes stuttering, but there is another important element that intensifies our stutter over time, which is fear of stuttering, which is a common mental disease and most people suffer from it. What your pychiatrist trying to do is to make you fearless regarding stuttering. Ive listened to my psychiatrist and dont run away from situations that requires me to talk alot in groups, so I participate in a group of friends (about 17 people) weekly to play Mafia, which requires to talk alot ! I stutter alot while playing but at least Im not scared of stuttering in a group anymore, and thats what my psychiatrist wanted. I encourage you to see both psychiatrist and speech therapist simultaniously.