Police officers do not always feel a need to come to the scene of an accident if it is on private propery, such as a parking lot. Generally after the incident a police report will only show the information you give and with no finding from the officer since he or she was not present at the accident site.

You are lucky that you have both pictures, witness and a person who admitted fault. With all of this factual information the at-fault's insurance company should pay for your damages. Once both you and the other driver speak to the insurance company you will probably speak an adjuster who may decide who is liable and will settle the claim.

How to Deal with Insurance Adjusters is an article that can help you prepare.