Document every conversation you have with management. Never speak to management when you are not on the clock and never without representation if you feel it will lead to disciplinary actions. Never go into a office with the opposite sex without another hourly with you no matter what the conversation is. Did I mention document time/place/context of every conversation you have with any member of management? Call your local and ask what else you could do to prevent this from escalating higher. If you feel like something is going on, it probably is.
Do all of these things and come back here in 3 weeks and tell me how much better it got for you.