If I am at blame, should I volunteer my guilt?

No. It is best, after an accident, not to say anything until you have talked to your insurance company and/or your lawyer. In many instances, you may feel that - initially - you are to blame, but you could learn later that the other driver as much or more at fault, for instance if you learn he/she was drinking. Anything that you say at the time of the accident to the other driver can legitimately be used against you, so you should stay quiet, don’t volunteer to pay for any damages, and don’t sign anything, except for traffic tickets. However, do cooperate with police officers, and don’t lie - just stick to the facts as you see them.