Unless you have an "admission" in writing, no one can assure you that you have enough evidence. Further, it is more than "enough evidence" - it is the credablity of the witnesses, and the organization to be able to bring the matter to trial, if necessary. The first step for you is to tender the matter to your insurance company.
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Go to the police station and get an accident report called a counter report. Also, report the accident to your insurance company to resolve. Never try to resolve a car accident with the parties involved, as it rarely ends well. Good luck.
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Based only on the above facts, I would say that you have an up hill battle. Hopefully you have something more than just a statment at the scene. Witnesses, documents...? Best of luck.
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Go file a report. You need to also contact an attorney about any potential medical claims that you may have. I definitely think that the opposing drivers insurance company will fight this matter since there was no immediate accident report
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