collision on freeway, rearend

Hi,

I was rearended while driving on 405S in Los Angeles. But the highway patrol report determined that I was at fault. They said the car behind me was already in the fast lane when I moved into the fast lane without safe distance.

The fact was that she had just moved into the fast lane and started to speed, while I was in the process of moving into the same lane (according to the witness). I checked before changing lanes to make sure there was no car in that lane. Of course, I wouldn't know she would be changing lanes almost at the same time. The report also did NOT mention that she started to speed.

I only have liability insurance. What should I do at this point? What are the chances of getting the highway patrol people to change their decision?

Thank you so much for your help!