Hey I'm a stutterer who became a doctor. I really struggled during the first part of med school but gradually found my groove. I did go to speech therapy when I was at my worst, and it got me out of the hole I was in, even if I didn't end up sticking with it. It absolutely can work for adults (just look at King George VI). I honestly wouldn't see a neurologist. Based on my own experience in neurology, there's very little they'd be able to do for you as there are no standardized medical treatments for stuttering yet. There are some meds that have shown some promise but still need further review. For me, the biggest thing was getting out there and exposing myself to more situations where I stuttered until I stopped caring as much. The big a-ha moment for me was actually during speech therapy when I realized there were things I actually liked about my normal stuttering voice and didn't want to replace with a fluent but artificial-sounding voice that wasn't "me." Self-acceptance is the most effective solution but it takes time to get there.