Yes, typically if you are putting a claim through the at-fault party's insurance company instead of your own you will need to file the claim yourself. Because you only have liability and not collision or comprehensive coverage the claim would be placed with the other (at-fault) party's insurance company.
In general, insurance companies do not help put in a claim with another carrier. If you had physical damage coverages of collision and comprehensive the insurance company may have helped to file the claim just in case it came back to them and had to be placed under your coverage for some reason (such as the other person's insurance was not valid).
Your insurance carrier would have certainly helped you file the claim if you were placing a claim through coverages you had, meaning if you had and were using your own collision coverage. Then your provider would have accepted the claim and subrogated with the at-fault party's insurance provider if they had to pay.
Our article Seven Steps to Filing Your Car Insurance Claim may be of help to you at this time. If you are in market for new auto insurance, you can get an affordable California car insurance rate here with us.