Well, you can understand why they're fearful and upset. If you had told them, you could have downplayed it, how no one was injured, you weren't driving, and the driver wasn't going that fast. See, it helps to tell the story first out of the gate. You really should have told them, especially given your parents' accident. Just own up to that and apologize, say you understand and you'll tell them first thing anything happens.
It's only a month, and may even wind up less than that. More importantly, though, they have to deal with their fears. I mean, you could die anywhere at any time.
Please be a little understanding of their fears and concerns; they love you, obviously, and want you to live a long life.
You'll be away from them all day at school, and if you have a bike, you could ride it on the weekends, etc. It's really not so bad, getting a ride to and from school.