Can I sue if a woman made false claims at my job and got me fired?

I'm from Georgia I had a job at a nursing home a woman found a bruise of a resident. She blamed it on me even though it had been 12 hours since I had worked with resident. She finally found it which meant 2 more shift worked with her but because she had heard gossip about me she assumed it was me who gave a bruise to the resident. I did not because if I had actually accidentally bumped her leg I would report it immediately but she decided to go to the front office accuse me of being rough wrote a 2 page letter about me to the office. Then went to the other residents family members and told them to say I was rough with their family member even though no family saw me be rough no other residents had any bruise but because of all this stuff she did. I was terminated for employment. Can I sue her for slander and harassment?