Do I have any rights as being accused of Harassment?

I am a male over 40 years old and I work with primarily women. I have known the accuser for about 8 months. I see her at school and work. She would come up to me and touch me on the back say Hi and I would do the same. Our work is can be very stressful and we help each other out. She was telling me how she was having a really bad day and that she was stressed. I went to console her as we have done to each other before, so I playfully grabbed the back of her neck and gently shook her and said it will be OK. She said stop and I did. The next day we were called into the managers office. She was asked her side of the story and I was told to put mine in writing. Next thing I know I have other employees approaching me asking me why they are being called at home and asked about me. I then get called to my managers office and get handed a corrective action to be put in my file for inappropriate harassing behavior and I am told if anything happens again I am terminated. They also were told that I hit her behind which is a down right lie! I am a gentleman. I have never and would never do anything like that. What are my rights? Is it OK for her to do it to me? Is it OK for her to talk to me about her sex life? Is it OK for the other women to rub against me and hit my behind? I put up with this behavior because I need their help and I do not want to look like a complainer. I am a nice guy and this has torn me up. I feel as though my character and name have been defamed. I would never do anything to offend anyone. I am happily married with children and the accuser is young enough to be my daughter. They never spoke with me and told me about the accusations and never informed me or involved me in their investigation. This will prevent me from furthering my career, applying for promotions within the organization and applying for other benefits. How can I get this removed from my record?