Can I sue a company that caused me pain and suffering for staying 24 hours in jail for somebody’s mistake?

I have an interlock device since April 2013 in my car for 4 months. I bought a new car in July 2013 so this interlock company transferred my device to my new car. I've been paying and going to this interlock place every month for monthly check. On February 2014, I got pulled over saying my license was suspended because of not having an interlock device. I showed the cops I have one but they won't talk to me. They handcuffed me and put me in jail for 24 hours. I was so scared and I don't think I deserve to be in that place. After I got out, me and mom went to licensing office and ask what's going on with my license. They said my interlock place reported that your interlock device was cancelled. We showed them proofs that I've been paying every month. But what happened is they forgot to report back to licensing when they transferred the device to my new car. So basically, I've been paying every month for nothing. I've been going to court for my case couple times losing my hours at work because my lawyer trying to contact the interlock place and they don't want to cooperate. My lawyer just need a letter from them saying they made mistake so they can dismiss my case. They finally submit that letter after 5 times in court. My public defender said I have a strong case to sue this company.