You may have missed your opportunity to get the police to help you. Once you leave the scene, and make an "agreement" between drivers to handle the case between you, then you may not be able to use the leverage of getting the police to help you. It is worth a try.
You MUST file a prompt claim with your insurance company. Most policies say "within 30 days".
If the person who is "at fault" cannot (or does not pay), you should have uninsured or underinsured benefits under your policy. This means that your company MAY increase your rates, or even drop you later, FYI.
If you have to pay a deductible, then make a claim in your local small claims court for that amount. Chase the bastard down, now that you have been put to all this trouble and expense.Ask a similar question