Older co-worker becoming passive aggressive
I'd like to start out by saying that this is the first time I've posted on this platform so I apologize for any mistakes.
I (21F) have been working with my co-worker (66F, let's call her Jan for privacy reasons) for about a year. I work in an office setting where she is one of my few main coworkers, and we both started around the same time. From the first day I met Jan, she was a little rude? When we were assigned our first minor task, I had asked her if she wanted to complete the documentation portion of it or if she wanted me to. Jan said she would do it. After a day goes by (we were not busy at all) and the documentation isn't done, I asked her if she would like me to do it instead and that I didn't mind. Her words were "I've been doing [this type of job] since before you were born and you don't need to tell me how to do it, smartass." I was like damn ok and kind of let it go. I didn't really know her so I thought maybe that was just how she talked.
Since we started working together she has always slipped in these little jabs about either me being a smartass or a know it all. I try not to get involved in her individual tasks and mind my business, but on multiple occasions she has made some mistakes that unless corrected would have escalated into a bigger issue, so I would help her correct them/ she would come to me and ask the resolution.
Fast forward to a couple of months ago: Jan had decided to go behind our manager's back did something that our manager had explicitly told her that we as a company cannot do. This lead to my manager getting in minor trouble with his boss. My boss had asked me directly if Jan had done what she did, and I said yes. I felt like lying to my boss would have compromised the open relationship we have and gotten me in trouble (I was not involved with what Jan did). My manager confronted Jan about a plethora of things (her frequent mistakes at work, her attitude, and the poor choice she made) and when Jan asked how he found out it was her that went behind our manager's back, my manager said that I had told him.
(It is important to note that our manager himself does frequent checks on our work and catches the majority of Jan's mistakes himself, and we have had other co-workers go directly to our manager when Jan messes up).
Since my manager spoke to Jan and told her that he got the info from me, Jan has become very passive aggressive/rude. She has refused to speak to me some days, deliberately embarrasses me in front of our other co-workers, unsuccessfully tried to get me in trouble on multiple occasions and has increased the name calling. The other day she called me a ""brown noser" in front of everyone at the meeting for saying I had completed our training (my manager had asked everyone at the meeting). She also keeps making petty remarks about how she knows "SOMEONE" in the office is a rat. The name calling and stuff is lowkey starting to hurt my feeling and making work uncomfortable. I really like this job but idk.
Here is my question: what do I do? Do I confront her or do I ignore her? Also, do you think I shouldn't have told my manager the truth/ should I apologize? I have never had any problems at my previous places at work so I don't know how to handle this. Pls help.