Hit and run accident advice??

So I was on my way to work when a car ran a stop sign and hit my passenger side and then she drove off. I was hesitant to call the police because my registration was expired, so instead I called the tow company that I know of. The tow truck came and I told him my situaton, we both agreed that I was screwed lol. As me and the tow truck driver started walking back to the truck to leave we stumbled across a licence plate (the plate belonged to the person who hit me). At that point I called the cops and filed a report. Shortly after I went to the hospital to get checked out.I had some stiffness and soreness in my neck and shoulder but they didn't find anything in the X-ray. The arrested the lady the day after. Basically what should I do next and what should I expect from our insurance companies. BTW I don't have liability coverage.....