Do i need to report that i had an accident in my car?

i skidded on the ice today and hit another car. the damage to their car was that i smashed their wing mirror and scratched their side door a little. my car was more damaged as it smashed my wing mirror and dislodged my bumper. we exchanged details and they've phoned their insurance to claim from mine cos my car skidded to their side of the road. but they've said their car is old, and has a small amount of damage. do i need to report it to my insurance company as they've reported to theirs? i don't want to claim on my insurance because i'm only 19 and don't want my insurance to go up loads for an accident with minor damage to both cars. i'd rather pay for the damage without getting the insurance companies involved.