holy crap. your story is almost similiar to mine. sorry to get off-topic. there was 4 cars involve. and this was still in the school's parking lot. white car, green car, me, and my friend's car (impala). i was parked but backing up so i can get out of the parking lot. but there was cars in front of me waiting for other cars to pass by, but somehow. this white car was backing up NOT LOOKING BEHIND HER. and so the green car got afraid too so he started backing up. and there it happened. the green car lightly tapped my chrome bumper. didn't hit it, but tap. and then there goes the white car hitting the green car also. and so there's more push to my car. and so. my car was pushed back and hit the car behind me. when i got off of my car, i went to the car behind me because he was my friend and so i checked up on him. when i got back to the front, the 2 cars left. so it was a hit-and-run. before the green car lightly tapped me, i honked on my horn to somehow tell them to stop, which they didn't. but 2 teachers on duty saw the accident. and so they were my witness. long story short, campus police DID NOT WRITE A REPORT. which i forced him to but he didn't. he said it was only me and my friend's deal only. but he didn't say anything about the hit-and-run. when i report this to the insurance company, they said "it's not your car anymore. it's ours" so i went to school to request for the camera, camera was down for the whole week!! so now, it's still under investigation. i don't know what to do yet i'm 19. and first year in college.
but to answer your question, yes, let your parents know and they will settle it. you should of told them to write a report. if not, call the county police. because if it was her fault, her insurance will pay for your car, medical bills, and you will get extra money. but since there's no report, the only way is, start saving up or ask your parents to buy you a chrome bumper. it's not hard to install. just unbolting and that's about it. good luck on your solution.