What would you gain by having this fight? If the charges were already found untrue, then the best thing for you to do is just forget about it.
You need to think very carefully before jumping into fights that you can avoid. They are expensive, and there is always the risk that you will lose and do more damage to yourself. Unless there is some specific way that a legal fight would help you (and fixing hurt pride is not a good reason), it is doubtful it is worth it.
If you think it is worth it, the first step is to talk to a good lawyer. You aren't going to get any good advice from an internet forum that I haven't just given you.
The best revenge is to live a good life. If you can put this behind you and forget it and focus on living your life, it is the best way forward.