AITA for cutting my best friend out of my life using the silent treatment?

Hello people! I've been reading and admiring reddit posts for a few years now but never posted anything. Now I really need to just put these emotions out there and see if I'm in the wrong here. Also using a throw away account because I have some personal info on my main profile. English is not my first language, sorry for any mistakes :)
So...here is the story. I (22f) have (had?) a best friend Kate (21f) whom I stopped talking to just yesterday. She was such an important part of my life and I loved her to the bottom of my heart. The only flaws she has are that she can be super jealous, possessive and insecure. I liked her nonetheless because she was mostly like that just when she was in a relationship, not with friends.
The problem started last week when Kate got angry at me out of nowhere. We were at college and she was fine for a few hours and then just changed completely. She became cold and mean, but I brushed it off as her being extremely tired and nervous (she said multiple times that she was tired). I went home feeling weird about it and realized I should probably talk to her the next day.
Next day came, I entered the classroom and she just said a simple 'hi' and started ignoring me and talking to her other friend, Anna, whom I met just a few days before. She basically gave me silent treatment for hours after that moment. Note: I have a narcissistic family member who uses silent treatment all the time and she knows how much I struggle with it. So I decided to talk to her after classes and was just being really nervous the whole day and overthinking about it. Like why is she behaving that way? What did I do? Did I even do anything? What's happening?
Kate came up to me and asked to talk after the class which I happily agreed to.
It ended like this... she asked to talk first and started talking about how I'm her best friend but she wants to have other friends, and how she is angry with me for being jealous and possessive over her etc. To say I was in shock was an understatement. I stopped her and asked where is all of that coming from. Everyone who knows me knows that I'm not jealous almost at all, it has been even an issue in my relationships because guys think I don't care enough since I'm not being jealous over them. I mean, that's not a good thing, right? On the other hand Kate herself openly talks about how she is super attracted to guys who are jealous and how she's also jealous and enjoys being that way etc.
She then accused me of rolling my eyes the day before at her and Anna and said she took that as a sign of me being angry they are friends. Not true at all, never happened, I liked Anna and even asked her to come with as to a bar that weekend. Kate then started talking about some more situations that basically never happened and was using them as a 'sign' that I'm jealous. I was just in pure shock the whole time. She even talked about how her boyfriend and Anna think she's in the right and I'm the one who's just a jealous pathetic friend.
In the middle of the conversation Kate realized she was in the wrong and asked for a hug and if everything was now fine. Obviously I hugged her but said it's not fine. I explained how much it hurts that she was thinking all of that, how she was just being mean, and also giving me the silent treatment was hurtful as hell.
Her answer? ''Well yeah, I know you're hurt, but you're the one who made me angry, so..''.
That pissed me of, not gonna lie...
Me: So what, you get to hurt me and get away with it? Even though you got angry for an imaginary scenario you put in your head? Also what's with the silent treatment and being cold the whole day prior?
Kate: Well that was the test for you. I wanted to test if you care about me and this friendship, and you failed the test.
Me: Why the hell you had to test me and how did I fail that test?
Kate: Well, you just let me ignore you so you obviously don't care.
Me: You had to test if I care about you after everything we've been through and despite the fact that you know how much I've put into this friendship? On top of all of that you're being mean on purpose for two days and now you're angry I didn't what? Cry for you and your attention?
She went silent and then started to kinda fake apologize, kinda just to get out of the situation.
And well... I forgave her. But not before I made her promise she'll never give me the silent treatment again and she'll talk to me anytime anything happens, like whatever it is, just to say it and we'll deal with the situation together.
That was last thursday, everything was fine since (we didn't see each other tho, but we texted).
Fast forward to yesterday (tuesday).
I came to college, she was there, hugged me, said hi and literally one second afterwards started giving me a cold sholder and ignoring me with some girl I never saw before. I was confused but moved to the side to not bother them and was looking at my phone until the professor came. Kate just walked past me with a head held high and walked into the classroom.
That. That right there was a breaking point for me. After that moment I never once looked at her the whole day yesterday and today. I've heard she was talking about me behind my back, but I don't feel like she deserves for me to give her any attention, run after her and beg her to talk and be friends when she just a few days prior promised to never again do the same exact thing that she's now done once again. This was not the first time that she put me through a roller coaster of emotions like this and I'm just tired. Despite all of that I can't shake the feeling that I shouldn't be ending the friendship this way.
So, AITA for cutting my best friend out of my life using the silent treatment?
PS thanks for listening to my ted talk, feel free to offer some help or if you don't feel like it just know I wish you a beautiful day (or night), kind stranger!