Can my government employer fire me for consensual verbal flirting?

A lady at work began a consensual flirting verbal affair. She announced I was her "boyfriend" and I heard her say on the phone "my biggest fan is here". Without saying a word to me, she suddenly reported me for sexual harassment. My employer took no account of my explanation that there was no harassment and fired me. I want my record cleared and to get my job back, and if possible have the county sanctioned. I am paid $15,000/year (on call, though I report to work every day and if they don't have a job just help out). I have zero job status, and do not date and am celibate. I say nice things to everyone, ladies or gentlemen. This is the first time anyone has begun a verbal flirting affair with me.