do I have a case?

I was involved in the accident back in May, a NJ Transit bus my car from rear end in the Lincoln Tunnel and caused the damange. According to NJ Tort Claim Act. 59 -- Individual person can present claim against the state department and agencies, but not Insurance company. As a result, I have to file claim directly for deductible and additional car rental cost while my automobile was in the shop for repairing. However, I have to file claim within 90 days from the accrual of the claim.

On Oct. 13, Liberty Mutual sent me a letter stating that my claim was submitted to Arbitration, and the arbitrator's decision was unfavorable. I called them back and learned that the info stated on that letter was irreverent to my case and I was told about this NJ Title 59, that was then I learned about the NJ Title 59. Now I have to go to a court to file a "late claim" in order to collect my expense from NJ Transit as it's been six months since the accidient happend. I questioned Liberty Mutual why they did not tell me about this NJ Title 59 earlier, so I did not have to go to the court,, I also asked Liberty Mutual to find a lawyer to assist me with filing late claim and they refused. They argued I did not send them the accident report, but I was never asked for such information and was never been informed it will be quicker if I request a report and send it to them. The info on the letter was also wrong. The other woman who was involved in the accident - her insurance company told her the procedure from the beginning, and she already got her claimed expense back from NJ Transit. I felt the person who handled the claim did not know the business -- I should have been informed of this NJ Title 59 at the very beginning, and I am very disappointed the way they handled their mistake. Now I have to go through all these troubles and doing all these on my own. I complain to my insurance sales rep but there is nothing they can do (or willing to do). I am in the process of finding another insurance company. Liberty Mutual did not do their job and is not willing to help their client to solve the problem caused by their mistake.

Do I have a case to sue them?.