There's currently a blizzard in Chicago and I was making a right turn at a intersection. There's a stop sign so of course I stop my car and I was driving slow due to the snow. From behind I felt an impact and it almost pushes me out to oncoming traffic. I immediately rush out of my vehicle to confront this driver. He apologizes several times saying he tried to stop, but the road is slippery. I check my vehicle for damages and there are several chipped paint, but no dents. I asked for insurance information and he drives off nearly running me over. I'm currently wondering if I'm covered by insurance since this is not my vehicle, instead it's my fathers. Should I file this?

Does your father's policy have coverage for Uninsured Motorists? Were there any witnesses? Did you at least catch his license plate #? Did you file a police report? (adds credence to your statement)

Your father should still be able to file the claim (there may be a special deductible for this coverage). YOU can't file the claim, since it's not your policy.

One other point - while it is true that your father's policy on the car applies regardless of who is actually driving it, you should be named on his policy if you are a family member living in his household. If your father has neglected to tell the insurance company that you are a driver in his household, they may use that to deny coverage for your accident.