Unless you have a camera that shows exactly what happened, the insurance companies won't do anything until they receive the police report that will determine who's at fault. My brother recently went through all of this....might take up to a week before all the paperwork is filed. My brother later spoke to the other parties insurance company to get a confirmation they would be taking care of it.
Btw, unless you can prove you received serious body injury, no injury attorney will bother with you. They will likely get a chuckle out of those accident pics.