Speech therapy can and does work. Regular therapy works as well. It's an over-simplification, but you're basically say "I need both medical and dental work. Should I go to the dentist first, the doctor, or both?" If you have the opportunity to do both, do it. With the right speech therapist / program, you can make dramatic improvements in a relatively short period of time. IMO, stutterers often attribute the cause of their anxiety to their stutter. IDK if I believe that. I used to, but I've come around to believe that the stutter and the anxiety aren't as simple as the horse and the cart. I really believe they're much more interconnected.