I kinda felt the same way you did. I think talking to your teacher will help put you in a little more ease. But ultimately in my experience, it's not going to help a ton because it's not as big of a problem as we worry about. I would just suggest you try to challenge yourself and your fears when you can (and even a little when you cant) and you'll be fine. Aim your focus at your work rather than you're stutter and you'll succeed.