Help! I was just in a crash

I just got into a car wreck. I'm home now, for about 30 min now and I'm getting ready to call my insurance company as well as the other person's insurance. I'm very shaken up and a little pissed off to be honest.

 At the scene, the lady (older lady about 70) agreed and said "no police report was necessary" (stupid on my part, I know now).

Please tell me what to do.  Should I call my insurance first or hers? In all honesty, if this was not me, I would have perfect advice for anyone else however, it's me involved and I am completely baffled and a little side stepped and I really just don't know what to do first. I'm still shaking (and mad). 

This is what happened: 

It's a 3 Lane Rd. I was in the left lane. It is heavy traffic on a clear, bright sunny day. I signaled and moved into the middle lane. About not even a minute later, I hear this crunch sound and simultaneously looked to my right hand side. There is a vehicle that has hit my car! I am completely inside the middle lane. (I did not halfway merge into the middle lane and hit an oncoming car that was already in the lane. I was fully inside that middle lane and was there for just about a minute before I was hit).  

So, I hear this crunch sound and look to my right hand side. There is a car that hit me, and apparently came from the far right-hand side Lane and entered into the middle lane that I was already in. 

As I look over, I see a car almost inside of my car, and they continue to drive forward for a few seconds. My windows are already down and I start to yell "stop, stop! You hit me!" The lady does not hear me. 

I blow my horn to catch her attention. My passenger side (front) door window is open, and is equal to her back seat window. She does not hear my horn initially or my yells to stop. Her elderly husband tapped her on the shoulder, as she is looking straightforward, and finally catches her attention. She looks over to me and I signaled to her to pull over as she has just hit me.  It took at least a minute for her to realize what she had done. She's looking forward and waiting to go with the traffic . As soon as I heard the crunch I put my brakes on but she continue to move forward which took off my passenger side headlight. If she would've stopped when she initially hit my car, there wouldn't have been as much damage to my car.

Anyways, she finally gets my attention and we pull over to the gas station which is on the right-hand side of us. I jump out, look at my car and I see the mess of my car which I did not expect.  I really didn't think it was going to be all that bad considering the sound and everything plus I didn't even feel a jolt.

I got out of my car, made sure her and her husband were OK but the first thing I had said to her was "you hit me"  when I approached her driver side door.

The first thing that she told me was "no, you hit me ". She proceeded to tell me how I changed lanes and I hit her.  FYI: When I had changed lanes no one was there....I remained in the middle lane approximately one minute before being struck by her car.  

I told her "I think it's best we called the police and make a police report ". I did explain I have insurance and everything and I wanted to exchange information in the meantime.  She told me no police report was necessary and we could just exchange information. She said the last time she was in an accident, in 1979, the police showed up and said "oh, it's two women "and said never mind.  At this point, I was just so pissed off and I just wanted to go home, so I said yes that's fine, we can just exchange insurance information. All her information was up-to-date and current.

No one in her vehicle was hurt, herself or her husband, nor was I. The damage on her car was scuff marks that went from her driver side door down to her passenger side door. The damage on my car is a huge dent (on the I guess it's a fender/ bumper) that area just in front of where the right passenger side tire is but in  front.

(See pics)

We exchanged information, I took pictures of her insurance card, her license plate, her drivers license and she hand wrote all of my information down as well. I did also take pictures of her car damage and I took pictures of my car damage when I got home

Yes, I'm kicking myself in the ass for not making a police report at the scene. No people even stopped as a witness or anything.

I know I'm overthinking this, but please look at the pictures below and tell me your honest opinion. When she told me I hit her initially, I knew she was wrong. She hit me and she kept going and didn't stop which took off my front passenger side headlight. It took her forever to even get her attention she had no idea she was just in an accident. However, her telling me that I hit her is putting a question in my mind. Did I hit her? Did I enter the lane and she was mutually merging at the same time?

This is what she told me when I had approached her car, she said "what are you going to tell your insurance company "?   I replied back "the truth, you hit me ".   She then said, we can just exchange information but just tell the insurance companies we mutually hit each other, that you went from the left lane into the middle lane and I went into the middle lane from the right lane at the exact same time and we just happen to hit each other."

I could kind of  feel there was something strange with the situation so I just agreed and said yeah sure that's what I'll tell my insurance company then.

I knew otherwise, she was wrong and I was right but of course now I'm overthinking things as I always do and I need others opinions. Please look at the pictures below and tell me which car do you think is at fault. Again, it's a 3 Lane Highway. I was in the left lane and had just entered the middle lane and she states now she was in the far right lane and had just entered the middle lane