Stutter definelty leads to social anxiety from my experience too, there is a herb in Chinese Medecine that clears up my speech to 80% or so whereas speech therapy, other therapies, nor theater class helped me speak. The main herb is Polygala Tenuifolia aka "Yuan Zhi" which for some reason just makes me speak clearly. If I dont take it my stutter comes back and i do notice more social anxiety when my speech ability goes away since I know i will have trouble saying the thing i want to say so i'd rather stay quiet and out of the social situation. I had the experience of taking clonazepam which relaxed the nerves but didnt affect my stutter and wasn't as helpful in resolving anxiety issues as simple chinese herbs. I also did acupunture combined with herbs for 2 years and that worked too, although its expensive each session it did clear up alot of other anxiety issues in me. Without acupunture now, just this herbs works for some reason.