Should I threaten my insurance company regarding the determination of fault?

Question Details: I have insurance in DE which is a no-fault state. The other vehicle ran a red light and hit the back right side of my car and now my vehicle is totaled. I have not been injured that I know of but it has been a week but my insurer still has not determined that the other car is at fault even though the other party received a citation. They are claiming that I did not look both ways before crossing the road even though my light was green and I had the right of way so they are trying to determine the % of who is at fault in order to determine how much they will pay out. The other vehicle has a minor dent in the front but was able to drive away from the scene. I had to get my car towed and is incurring expenses, I have been out of work for a week, I have missed my daughter's sports tournaments. I have travel expenses from having to get a ride to get where I need. What should I do? If they claim I am 49% at fault and the other one 51%, should I appeal or get a lawyer for all the other issues that I have experienced because of this accident?

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