Insurance adjusters don't have to read you Miranda rights
Everyone who has ever watched TV must know that if they are ever arrested, they have the right to remain silent. The U.S. Supreme Court acknowledged in the landmark Miranda case that average citizens, when confronted by police authority, could easily be intimidated into making statements they would later regret. Thus, in matters of criminal procedure, police are required by law to remind suspects that it might be in their best interests to refuse to answer questions.
Unfortunately, no such requirement exists in the realm of personal injury law, particularly when automobile accidents occur. If you are injured in an auto accident, it is likely you will be contacted by the insurance company representing the other driver within 24 hours. Even before you have had time to fully assess your injuries or think about what happened, an insurance adjuster may pressure you into answering questions or even taking a settlement check.
For average honest people, it is difficult to tell that polite voice at the other end of the phone in no uncertain terms that you are not going to say a word. But that is exactly what you should do. You may feel compelled to tell your story, but this is not the time. Even if you have done nothing wrong, your situation is not unlike that of a person under arrest. Anything you say, can and will be used against you. Plus, it is the job of that person on the phone to sweet-talk you into accepting a minimal settlement right away. Do not fall into the trap.
The person you should talk to right away is an experienced auto accident personal injury attorney. Then, if you are contacted by the insurance company, tell them you are represented by an attorney. That is almost guaranteed to end the conversation.