Did you find a lawyer to handle your comp claim? There are still some lawyers out there who do. After worker's comp was "reformed" in the early 90s, most of us quit doing that work. You likely need to appeal the determination. I suggest doing some internet research and finding lawyers in Houston who handle comp claims.
I am not intending this to be legal advice, because I don't know the particulars of your situation. Call me if you would like to discuss this or other isues.
You can sue the State of Texas, but you cannot win. The state is immune from liability under the doctrine of "sovereign immunity" with a few very limited exceptions. Your case does not fall within any of the exceptions.
Rather than suing anyone, I suggest you address the merits of your workers' compensation claim in the proper legal fourm, assuming it is still open. To do this, you will need to hire a lawyer who has expertise workers' compensation law.
I'm still trying to figure out your first sentence. Worker's Comp claims are filed with the Texas Workforce Commission. You say you filed a "complaint". Do you mean a claim? It sounds like you filed a claim, received benefits, and they have expired.
DISCLAIMER: This is not specific legal advice and does not establish an attorney/client relationship.