I Was Recently In A Car Accident Which I Thought Might Have Been My Fault. I Told That To The Police As They Arrived On The Scene. Afterwards, A Friend Told Me I Should NOT Have Said Anything. Is That True?

Yes, it is best NOT to admit responsibility for the accident at the scene to the police and others involved. If there is litigation, anything you say might be used against you. Although you might have thought the accident was your fault, you might find out later that the other driver was to blame or that both of you were at fault for the accident. Be careful here. You should be honest with the police and/or others about what happened and the "facts" surrounding the accident, but you should not offer your opinion - in this case your opinion that the accident was your fault.