There's a serious disconnect between this...
She's like, "oh really?" But she didn't seem like she reacted too badly. And her tone was a normal, conversational tone.
and this ...
Still, I got the sinking feeling in me that I said something wrong.
Stop being so paranoid. Even if this is true:
Will she start talking shyt to other ppl about me?
Give up on her. She'll never be your friend. She isn't worth the effort in stressing over how and what she does and thinks about you.
If so, what happens? Maybe my supervisor would know the answer but b4 I bother her, I thought I'd post here.
It's a catch 22. You're damned if you do report her to the supervisor. What can the supervisor do? Tell her to be friends with you? This isn't elementary school but a workplace for adults. Most supervisors don't want to deal with this melodrama or wouldn't know what to do in the first place if they wanted to reduce that kind of melodrama at the workplace. You're damned if you don't tell the supervisor because you will forever be obsessing over this nonsense.
The best thing you can do is stop obsessing over the cattiness or perceived cattiness of your coworkers and eventually find a new job with new coworkers. Use what we taught you here regarding social skills and the workplace in that new place of work and start from scratch.
Very little can improve where you work now. Presently, obsessing over this nonsense and acting on it will only make your work environment and your life with those coworkers worse.