You should first check the u-turn laws in your state to see what they say specifically.
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I am not a legal professional, but in my opinion you have a few. If you can't afford a lawyer, then you could try to argue it yourself. I would read up on the U-turn laws of your state and see if there is any feasible way you could argue that you should not be charged. You could also take a defensive driving course (on your own or judge-mandated) which in some states can remove the points from your license.
It is impossible to say the chances of getting the charge dismissed or reduced, but there is a better chance of this happening if you have legal representation. They know the laws and legal system much better than you and can greatly help you through the process.