A coworker doesn't like me. She points out all my faults. And the mistakes I do make she blows them out of portion. Gossips about me. What can I Do?

She must be insecure and jealous. Confront her. Ask her what is going on. And report her behaviour to your boss and to Human Resources. She cannot do this. People need to talk to her. Stop it now before it escalates far worse. And let me know what happens. Be calm. Be firm. Stand up for your rights.