Are there repercussions for suing a state owned agency?

im a longshoreman in a union in VA. The company i work for is a private state owned agency. They recently fired me for something, and when i read the contract between the union and the agency, they clearly have broken it. They said i will get my job back but that has been a month now and im still waiting. I asked for back pay, seeing as that they were completely wrong for firing me in the first place but was denied. Does it sound like i could sue?