Accident at 4 way stop(w/ stop signs), i had the right away

Hi Community, I just found this website today, and have read a few posts, everyone seems very helpful, and I am in sure need of some help. Setting: Last Friday, I was involved in an daytime accident at a 4 intersection (with stop signs in all directions) in a residential area in Southern California. There is one lane for each direction. I was traveling southbound and came to a complete stop at the intersection. There we two cars to my right, going east bound, nobody coming from the south or east. The first car proceeded to onto the intersection, which meant it was my turn to go next. As I crossed the intersection, I look to my right side, and see the second car coming at me. I was already 2/3 of the way across the intersection as she started to go. She hit my rear tire and rear fender. The lady was elderly, and she was more hysterical when we first pulled over, and kept complaining that someone had hit her just a few weeks prior and that her she just had her car fixed. I called the cops to ask them to come out and write a police report, but at the time she apologized for hitting me and that she didn't see me. The cops asked if she was complying, I said yes, so they said they did not need to come out. We both said we would call our insurance agencies that day. I had a passenger in the car, she did not. We did not have any witnesses. Post Accident: I filed the claim with my insurance company. They told me that since I did not have comprehensive insurance and only liability, I would have to have a claims adjuster from the party's insurance agency assigned to me. They called the other insurance company to notify them of the claim. I called the other party's insurance following day to find out the progress, and when I spoke to the claims adjuster, she told me that her client had claimed she had the right of way, and is claiming no fault. At this point, I was flabbergasted because she had claimed fault at the scene of the accident and now she is claiming no fault. She was not very nice at all. I asked if I could have the phone number of her client so speak to her about the situation, and she exclaimed to me that it would be considered harassment on my part. I was very friendly to her on the phone the whole duration. I called my insurance company; they escalated it to a dispute. But my insurance company said that since I donÂ't have comprehensive, they can't do anything for me, but to fight the liability issue of it. He told me that I should go to small claims. At this point, he took my recorded statement, and said he will contact the other party, or try to (since he did not her phone number). The other party's insurance agency has not even called me yet. I have a few questions to start with. 1)What are my options at this point? The damage to my car is not too severe, but I do not think it is right for her and her insurance company to get away scot-free. 2)What happens to my DMV record, if the insurance companies can't reconcile? 3)What are the insurance companies doing now? I called my dispute claims officer and left a message; he did not call back. I don't feel like he is too concerned for me, because he is not fighting for me, but rather if they have to pay the liability. 4)Related to 2, Is my insurance going to go up if this isn't reconciled? I am really grateful if you made it down this far to read all I have written. I am only a 4th year college student, and do not have the resources to hire a lawyer, any help here would be greatly appreciated, and I thank you in advance. If you have any questions for me, or need pictures, please feel free to ask, I will provide as much additional info as you need.