USMC SSgt got an OTH for charges out in town

I was an 11+ year Marine who was given an other than honorable discharge because the State of Arizona charged me with 5 felony counts of sexual exploitation of a minor. I was charged Feb 2008, OTH in July 2008, charges dropped Jan 2009. The state just dropped the case because there WAS no case. There was a woman who lived across the street from us on base who made 24 seperate complaints/charges against me. All were investigated by NCIS/CID and none were found to be truthful. This woman was crazy.
What can I do at this point? I have not gone to the VA yet. I am contemplating a libel/slander civil suit against this woman because she instigated it all.
Is there a way to appeal the whole discharge since it was based on crimes that never happened? I told my chain of command this before I was booted but they thought I was a scumbag because of the nature of the charges against me. Also, what is the best way to "clear my name"? All except close friends and family think I'm a piece of s@*# and I can't find a job.