Can I sue my employer for creating a hostile work environment and lying about my work performance to get me to quit?

I have been working for a small company for the past 5 years and the last 6 months have been total hell. My supervisor has been lying to the owner that I am not doing my job and when I confronted her about it last week she claimed that the log I fill out was not and had gaps in it, in front of the owner. I told her the log was completly filled out and to open the log and see for herself. She claimed she was just in the log and it was not in there. I finally told her to go in and I could show her that I was not lying and that the comments were in there. She did not go into the log right then because she knew that I had called her bluff in front of the owner and had caught her in a lie. She is also trying to make an issue of a Doctor appt I had where I left work at 10:30am and returned at 11:30am and considered it my lunch hour. I have taken lunches in the past as early as 10am in the past and it has never been a problem before. She is now saying that for every appt I need to request time off in writing and that 10:30 is not an acceptable lunch time. However, there are other employees who are friends with my supervisor who come in late, take lunch and leave early. There is 1 employee who takes 3 hour lunches twice a week and her regular lunch hour the rest of the days. I feel like I am being picked on and being forced to look for another job as they are unfair and show favortism to select employees, but choose to nitpick the rest of the employees. And the owner and my supervisor are having an affair so I can't talk to the owner. Besides, the owner hates confrontation and has my supervisor deal with any and all employee matters.

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