if yes, you are responsible for the damage to the 1st car and the front of your car.
and you need to report to your ins comp.
if no, the 3rd car is responsible for all damages. if you have collision coverage, report to your ins comp. and they will help you. if you don't have collision coverage, try to get a police report and send it to the 3rd ins. comp.
anyway, the 3rd car is responsible for the damage to your rear bumper.