Accident In Parking Lot

So I was involved in an accident in August. I was returning to work from letting the dog out as I do daily. Anyway, to enter our parking lot, you nearly have to stop or the car will bottom out. Got into the lot and didn’t see anyone there. As usual, I glanced at our shop- make sure the parking signs are straight, planter looks good, any trash or cig butts I need to pick up.
It was just starting to rain, so I assume this girl ran out between some cars. I obviously didn’t see her and she ran into the right side of our car by the passenger mirror.
Of course I freaked out. Stopped the car to see if she was alright. Said “OMG you okay, sorry bout that!” She was with two men (one was her husband). She got up and walked around a bit. I was immediately giving my phone number to one of the guys, maybe both. It’s now raining a little more. I pointed to our business and let them know that’s where I can be found.
She says”my leg hurts. Take me to the hospital!”
They all jump in the car and drive off. Leaving me standing there in the rain thinking we’d be doing the police report. That didn’t happen.
After a few , they want my insurance info to pay her medical bills. I call my agent and then claims to tell them my story.
I get a text yesterday saying that my insurance won’t pay her bills because I didn’t outright say it was my fault. She’s seeming nice and just wants the bills paid and this to be done amicably. She said she doesn’t want to pursue legal action and suggests I call my insurance company again “ to work it out”.
The insurance company (Allstate) is confused/ surprised really that there’s no police report.
I even mentioned that I could charge her for hit and run since they left the scene. Insurance company, said “probably so” They were there probably 90 seconds.
My agent and claims both said “This really strange”. I guess referring to lack of police report.
I have no experience in situations like this and any thoughts would be GREATLY APPRECIATED.
I’m also caring for my wife who’s got Alzheimer’s, so between that and Thanksgiving coming up, I’m quite overwhelmed.
Thanks in advance. Very much!
Location: Bham, Al