You should not have a problem locating a personal injury attorney willing to provide you a free consultatiuon regarding your case. If the two of you decide to pursue your claims, you should be able to enter into a contingency contract with that attorney. He or she will only be paid if you recover from the restaurant for your damages.
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There is probably a fairly strict immunity statute applicable to your case. You will almost certainly have greater recourse by contacting your local school board.
To receive proper responses, I would definitely repost this question under a different heading, such as subrogation or medical liens. State statutes usually address the various types of liens and the proper enforcement mechanisms, including the applicable statute of limitations. These are unique to your specific state.
If you have your own car, you probably have liability insurance coverage. Provide the other car owner with your insurance information and have him make a claim. Do not pay for the damages on your own without obtaining a full release of all liability. Your insurance company will make certain all the proper releases are executed.