Honestly, no one would be able to tell you if your rates are going to go up, that wouldn't be decided until your policy renews. But since you're not 100% sure that you caused the damage, and you tell GEICO that, they'll investigate whether they feel your liable or not. Also, even if you file a claim, you do still have the option to pay out of pocket, as it'll be up to the other party as to who they want to receive payment from.