If I got into a car accident without insurance but it wasn’t my fault, what should I do?

Contact the other driver's insurance carrier to be compensated for your damages. You can collect all out of pocket damages car repair, rental car for reasonable period of time, wage loss for time lost from wok for injuries but nothing for getting the rental car, medical bills but nothing as to pain and suffering. The insurance company may fully accept liability even if the other driver is trying to go after you for payments. If the other side is represented by an attorney, send an e-mail to the attorney [or the other driver/car owner if not represented] stating all the helpful to you facts of the incident, that you have no insurance coverage nor assets [if the latter is true], and that you will not offer any money for a case in which you are not at fault. Unless the other driver suffered significant injuries, their attorney will likely tell them to drop the matter as they will recover nothing and the attorney, knowing they will get no fee for their work, will not want to handle the matter.