Can I sue an insurance company for monies lost after they denied my claim?

First of all you need to do whatever you can to get your car out of the body shop. The additional daily storage charge is not something you can easily get reimbursed for if at all. Furthermore, some states have laws, like in Kansas, which gives the shop owner the right to sell your car in if is not redeemed within a certain time period. Secondly with respect to your first question, no you cannot sue the insurance company. You do not have a claim against the insurance company since they were not a party to the incident in question. Any suit you file would have to be against the other party involved in the accident. You say your light was yellow, the other driver says your light was red, and the police were not there to actually say what color the light really was thus what you have is a question of lights case. With respect to the issue of who was at fault, based solely upon the lights issue many juries would find each driver 50% at fault. In Kansas no one would be able to collect anything since the law requires a party to be less than 50% at fault in order to collect from the other party. In Missouri a party would be able to collect 50% since Missouri allows one to collect on the percentage of fault attributed to the other party. However, you were north bound and the other vehicle south bound making a turn in front of you. Most states have laws placing fault upon a party that makes a turn in front of another party. There are many unstated factors that need to be taken into consideration which may have a bearing on the outcome of the case thus you should seek legal counsel to help get you the relief you need and desire.