A follow up email certainly doesn’t hurt if anything it shows you really want the job. Don’t put yourself down from stuttering though. That is part of you and you can do is try your best to manage it. Personally I just went through a job interview and stuttered a lot yet I still got hired. His reasoning is because my resume showed I was qualified and he felt my answers were “genuine”, his words. My advice if you get it great! If you don’t just learn from it but don’t put yourself down for it. Good luck 🍀