Hey Clover,
Your teacher may not excuse you from the assignment if you talk to them but if you let them know maybe they could work with you personally, 1 on 1, and help you overcome some of your anxiety issues.
I used to have problems speaking in front of crowd. I had a speech impediment for a long time. I think the only way to get better is practice.
Read to your family, read to your friends, read to anyone who will listen at first. Read in front of a mirror so you can watch yourself, read aloud to yourself.
I think if you do those small things and work your way up to going in front of your class you will be okay!
- R