The short answer is that yes, you can be sued. Will the other driver sue you? Maybe.
You should make sure your parent's insurance doesn't cover you, it may.
If you are contacted by the other driver's insurance provider or attorney, don't make statements to them. Get yourself an injury attorney and follow his/her advice.
You also have to worry about criminal/traffic court. You need to retain a lawyer for that.
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I suggest you speak with your cousin about what insurance he had in effect at the time of the incident. Depending on the provable facts, you may have coverage through his policy.
I suggest you not publish anything further on the Internet about this incident and seek counsel if necessary.
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Mr. Lundeen is licensed to practice law in Florida and Vermont. The response herein is not legal advice and does not create an attorney/client relationship. The response is in the form of legal education and is intended to provide general information about the matter within the question. Oftentimes the question does not include significant and important facts and timelines that, if known, could significantly change the reply and make it unsuitable. Mr. Lundeen strongly advises the questioner to confer with an attorney in your state in order to ensure proper advice is received.
This ans. does not create an attorney/client relationship.