I'm not an attorney, and am familiar with only the laws here in New York, but one thing I'm pretty confident in, is that you made a mistake in judgment by not staying at the scene and requesting police intervention. Especially when your car had visible damage, and it can safely be said you hit another motorist from behind.

A police report is the sole evidence your insurance company has to defend itself in an action against you. Even if you didn't think the damage warranted the police, you now understand why it's important to also consider the potential for future medical liability to either yourself or the other party.

It could be said that either, or both of you are guilty of leaving the scene of an accident. If true, your insurance company may deny the claim. But again, I am not an attorney.

I would suggest that you make two phone calls. The first to your insurance company explaining the details and the second to an attorney in your area who specializes in motorist/accident claim cases. Advice from either of them may lead you to your local precinct where you may have to do some paperwork.

Lastly, I don't know how a AAA claim fits into this equation, unless they are the other parties insurance carrier. Either way, it's best you contact your own insurance provider and explain the details. You might also want to take pictures of your vehicle and the scene of incident, and if possible, if you have the information, of the other vehicle involved.

Did you not at least exchange information with the other driver?