You're not a scaredy cat, it's a nerve wracking thing to have to do for yourself, what makes it worse is not having seen many people do it before you because it is so nerve wracking. I think her reinforcing pronouns on you that are not yours is her actively trying to make sure she can still use them and not face any consequence for it. Like some teachers do "I'm right, you're wrong, shut up." which is very much not the truth here.

I am so sorry you have to deal with a teacher like this, I am glad your partner in the class sees this to because it means you're very much not alone, other people are seeing it happen.

You're never weak or unprepared if you can't get yourself to say what you want to right when you're put on the spot. Opening yourself up like that again and again can be extremely exhausting and draining. I get it.