Even though you were the driver at the time of the accident since your friend owns the car and thus is ultimately the one that is concerned about the repairs to the vehicle your friend should place the claim with the at-fault person's insurance company.

You will need to be available for the at-fault party's insurance company to speak to so that they can get your statement regarding the accident. It will be helpful for the claim if there was a police report placing the girl that hit the car at fault or if you have other witnesses stating the other party was at fault.

If for some reason the other person's insurance does not pay on the claim then your friend could then see if he could place a claim with his or her own collision coverage.

Just for future knowledge, if you were at fault in this accident it would be your friend's insurance as the owner that would have been primary to take care of the other person's damages. If your friend's limits were exceeded then your liability insurance would be used as excess or secondary insurance.