Texas Liability Insurance Company Who Desides Liability?

Who desides liability? - texas liability insurance company

I was involved in a car accident, no injuries, the other drivers do not yield right of way. Another driver was zzzoooommmming three lanes to get to a grocery store, I could not stop and front passenger (under headlamp) of my car on the rear passenger (right) behind the wheel of your car. If I 1 / 2 second. Today, insurance companies have decided to take charge. I requested the inclusion in this conversation and denied.
What can this be true?
The other driver from his vehicle and said: "I'm sorry I broke the car, sorry." I say that a verbal response to a situation.
The police have not intervened to ask here in Texas, they would tell us that the exchange of information and by the insurance companies to resolve. I've heard of a ticket is not available, everyone's responsibility, by other units of the insurer. If you do not like the decision, what can I do now?
What rescue insurance can do for me ????.... haha