Get a lawyer or some council that is reputable, and go o court dressed very nicely (for example look very normal, polo and khakis etc) and have your council ask for probation where you cannot get a ticket or an accident for 6 months, and if you do the wreck will go on your record, but if you don't it could be thrown out. this will be to prove that this is a one time thing and that you are just young and inexpierienced, offering to take drivers ed is not a bad idea either.
Of course the claim will be on your insurance so to some degree it will never be removed from your record as far as the insurance company is concerned. So it might not really be worth your time, because your rates will probably go up weither way. Try asking your insurance company and see if having it removed from your record will make a difference.