If I was falsely accused of theft by a co-worker, what are my rights?

Question Details: Girl lost ring at work. There is security footage of my ring falling and off my finger and me picking it up before the girl's item went missing. The camera was not of a good enough quality to differentiate between the rings but I have proof of my own engagement ring clearly needing sized. I was humiliated and made to look like a thief. Lost out I work, worried of criminal case against me. Then the girl found her ring on her own accord. Can I sue her for lost wages? I would have settled for a public work apology but failed to receive one.

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