It was smart of you to ask about your sick calls, most employees wouldn't give a rip how they looked, even with the gossip, so long as they got away with it.
She doesn't sound very professional, saying she doesn't like you. Your HR people would not like that!
It's hard to give helpful advice without knowing more about your supervisor. But if you're in bad with her and with other employees, yes, you could be on the way out regardless of your performance. I've seen it happen, to a guy who was an icon in our industry and had worked for the company for 25 years, but he made things difficult so that people didn't like to work with him.
It's time for you to shine, keep your head down and focus on your work, give a little more than expected, bring cookies on Monday, etc. I'm not saying to brown-nose, but just show a sincere interest in helping the company and making everyone else's job a little easier.