The fact that you've already notified your insurance provider about the incident means that your rate is likely going to be impacted if you're found to be at-fault regardless of whether you choose to pursue the claim or not. As soon as your company becomes aware that you were involved in an accident, that information is documented. As for fault, that is actually determined by your insurance company so you may still be considered not at fault depending on the details of the incident. Since you've already told them about the crash it would make the most sense to file a claim
rather than pay out of pocket because you won't be able to avoid a change in rate by paying for the repair yourself.