A woman tries to blackmail me

I am separated from my spouse and leading a lonely life. I created my profile on a matrimonial site where I met this woman. We messaged each other. Soon our friendship matured into love. She suggested outing on weekend. I agreed. She sent me details of various hotels on a hill station. I booked one of them. Before that I asked her about stay. She said she would like to stay with me and share the same room. Accordingly, I did thinking that we both were mature. (I am 42 and she is 32). She said hers was divorce awaiting to which I didn't object at all. Mine is a clear case. I have to pay alimony to my wife for which she is in contact with me. The affair continued for a while when we went to a beach to spend another weekend. Meanwhile I told her everything about me including my office place phone no home address etc but she did not tell me anything about her residence or work place. We got back on a Sunday evening and then she started to avoid me without telling me any reason. I was so emotionally attached to her that I hardly could bear her parting. I tried to contact her but she didn't respond. So I sent her sister a message on FB telling her whatever happened between us and how desperately I wished to marry her sister. Then I got a call from her threatening me. She also called my authorities and asked them to take action against me. Since I am govt servant my authorities issued me a letter demanding explanations on the matter. It is because she told them that I harassed her sexually and demanded six lakh rupees from her. It was very difficult for me to come out of her. One day she called one of my ex students and sent him screenshots of our chats. She sent only that part of chat that was in her favour. That ex student recorded her call and tried to manipulate me asking financial help to expand his business. I am trapped anyhow I want to save my job. She already has ruined me socially and financially. My ex student doesn't know about my personal life. He told her that I am already married without getting it confirmed from me. She had had his number because once I called her from his number as I had my batteries discharged. She now threatens me to take action against me under IPC 376. Kindly help me.