I wouldn't do it. It's much too personal. Remember, she is supposed to read / review it in front of all the class. That'd be rather embarassing for her as she seems to be as shy as you are. And making her feel that uncomfortable would be the safest way to kill the relationship before it even started.
Write her a different story she can work on and give her the personal story as a present. You can say it's in return for the hug.