The first thing that needs to be done is to call the police. Even if you have to wait a while, wait for the police arrive. They will investigate and determine exactly what happened, who is at fault and put all of the pertinent information in their final report. They also will put a diagram of the accident scene in the report showing where the vehicles collided and where they came to rest.
All of this is very important. It provides a record of when and where the accident happened and who was involved. I have had clients consult with me about having an accident where they were injured but did not call the police. They exchanged information with the adverse driver and then left the scene. When I would contact the at fault driver, they would claim they knew nothing about the accident, they were out of town on that date etc. Without the police report there was no way I could prove a claim against them. Even if you have a passenger in your car who was a witness, it is still your word against theirs.
Also, if you have an iPhone, take photos of the scene and the position of the cars. Many times the cars are moved before the police arrive. Most of the time there is disagreement as to what happened, who was in which lane and who caused the accident. Photographic proof goes a long way in establishing who is telling the truth regarding fault and responsibility for the accident.
Always report the accident to your insurance company. They have the right to know about the claim and failure to promptly advise them could violate the policy provisions and result in a denial of coverage. Your insurance company will help you with your claim against the other party and their insurance company.
On the other hand, the adverse insurance company is not your friend. It is their job to show that you were at fault, you were not injured and try to minimize the amount of compensation they have to pay you to settle the matter. If you give them a recorded statement, it will be used to discredit your claim. Think twice before speaking to them.
Better yet, call me for advice on how to proceed. The consultation is free. There are many issues to consider in successfully prosecuting a personal injury claim and a possible lawsuit to be fairly compensated for your injuries, lost wages, medical bills and your pain and suffering. The insurance company has attorneys. I would suggest you retain a lawyer to level the playing field and make it a fair fight. Nothing is owed to me unless and until we prevail and you are compensated for your damages.