Based on the fact that you received a ticket for the accident, the accident will be listed on your motor vehicle report (MVR) regardless if you file a claim or not. Having the accident on MVR means that your insurance rates will be impacted even if you pay out of pocket for the accident. Your rates may not increase as much but either way they will still increase. Another factor to consider is some companies will drop you at the time of the renewal if you've had a certain amount of claims within a short period of time (within the last 3 years). Every company is different so you would want to check your specific policy to find out what their terms are. Here
is more information on when you should consider not filing a claim. If you do decide to file a claim, here
is information on what to expect.