I do not believe I was at fault in the auto accident. Should I use my own collision policy or try to collect from the other party?

A lot of insurance companies will deny a claim even when their insured is at fault. If you have one of the better insurance companies they will help you out and take care of the claim and then subrogate back to the other insurance company to get your deductible and other money back.

NOTE: See Collision Repairers Select Insurance page for list of top insurance companies.