Is she lying about being hurt in a crash to make me feel bad?

This is too difficult a situation to determine the correct answer for you. It's all up to you. I would say to explain to her that you need a break from her for a while and a chance to get over her. The only way the two of you are going out together is if it's on a date. That otherwise, you need your space. It's not fair for you to have to go through it all.