Not a doctor but a short time using SRIs worked for my stutter 25+ years ago. Not because they removed the actual act of stuttering but because they gave me a breather from the anticipatory hell of it and the post stutter internal reaction cycle which then allowed me to deal with the vocal mechanics of adjusting my speech in ways I had never learned to do at the point in my childhood where every kids proto stutter usually disappears. I still stutter, you just can't hear me do it very much, I don't get over anxious about it and spend a lot of time presenting to large audiences without ever even considering it as a potential problem. A lot of people are going to tell you no drugs can help you, might be true for them or you. Wasn't true for me although I'd 100% agree that not caring about what others think is one key to not stuttering. The other is conciously understanding how each sound is made. Anyway it changed my life but it doesn't work on its own, learn how you are supposed to make the sounds you struggle with and practice them like you would a golf swing.