I was hit by a car and the driver asked me to not call the police and exchage our insurance information. It turns out that she doesn't have one

Unfortunately, this is a very common scenario. Contact your insurance company and report the claim.  If you had collision or uninsured motorist coverage, they will get the repairs started or contact the other driver and get the insurance information. I actually wrote a blog post that explains your situation more thoroughly. Either way, don't ever do that again.  Always get all the information at the accident scene.  If the other driver refuses to give you the information, just call 9-1-1 and tell them to send an officer out to facilitate the exchnage of information.