<human>: Can you provide a brief overview of the text?

CA, State farm.

I was backing out of my driveway at 5mph and hit a moving car (maybe 30mph) going along the street. My car has a big scrape along the back bumper with a circular part (guessing the spot for towing?) missing and hers is the typical scrape-in/deformation for the side doors. 

She was in a rush (just had a stroke and couldn't think well) and I was in an emotional rush from the accident and late to work. She asked for name, cell #, and insurance info. I gave her that and wrote them on a paper for her since she couldn't write well or something from getting out of the hospital from just having a stroke. 

I asked for name and cell # and she said she couldn't find her insurance currently so she would give it when she would get her insurance to call my insurance.

Upon leaving, I realized I fked up majorly both on not looking more carefully and on not getting more information. What else should I have done?

Here's my current reflections:

Neither party got Drivers license information (I could have faked the info I put down if i wanted but I would never do that.)
Neither party took pictures (wow I'm feeling stupid)
Neither party filed a police report due to forgetfullness or rush (unaware of repercussions of this -- I'm assuming it's illegal and we may get in trouble?)

I failed to get her insurance info (not sure what I should have done if she claimed she couldn't find it currently )

Please feel free to add and correct any of my mistakes above ^

Lastly, what do I do now? Do i play the waiting game? What should I be expecting the next moves to be? I'm going to set off a few thousand in cash to be ready to pay for some damages that insurance always seems to not be able to cover. All I know is a deductible is something I have to pay and hopefully the insurance pays the rest, and then my insurance prices shoot up for me getting in an accident :(.

This is my first accident so I want to learn from this and follow procedure properly in the future.
<bot>: backed out of driveway, hit a moving car, some damage on my bumper, some damage / indentation on her side doors. WE fail to get each others information immensely. Now i dont know what to do.