DOUBLE Jeopardy Laws Question?

I need a clear understand about Double Jeopardy laws in the state of Texas. I was recently sued by the TX attorney general in the matter of a minor child. I hired an attorney and if I win my case, can she try me again pursuing the same matter? Or, is it once its done, then its a done deal? Regardless of the outcome, win or lose, she can not sue me for the same matter again? I'm not sure if this is even considered double jeopardy, however is there anyone out there with the answer? And if so, is this a true statement?