Can someone tell me what's the case here?

So, I have been dealing this girl for 6 months. She is my classmate. And we came from same city. For first 2 months, we literally had some sort of connection. Now what happened, after 2 months of talking and meeting in classes, i didn't want to ask her out because i kinda wanted to delay, but she was the first one who approached to going our city together. So, after we agreed, the day before we were going, we had an argue where she said, "who are you tell me what to do or not do". So as she said that, i didn't go with her though she texted me, and i said do whatever you want. After that day, she stopped talking to me for weeks, and when i said to her what's going on? and we kinda argued again. After this i sensed pull back, and finally i stopped talking to her. I didn't talk to her for 1.5 months.

When ignoring, she wanted to talk to me but didn't because i was ignoring her. So, finally i did talk in texts but she was cold and rude and when i said if she was angry that i didn't talk to her, she laughed. I said you have so much friends and and a boyfriend (she actually didn't have and i knew it) so it's okay to gain some sympathy. So, i asked her if she wants to home with me and she denied because she had exam. But later on, she called me to go with me and i agreed. So, what's more she told me what i wrote to her she showed these to her two male friends (and both of them are my close friends too and one of them wants her and i know it. And the problem is, they do get along well) 3 of them laughed seeing those texts. After going home, she posted a story saying "women like effort". So, i said for whom she posted that story she said you. After some chat, i confronted her for made fun of me to my friends she said don't talk to me i feel annoyed and i told her that's not sarcasm it is disrespect. she saw but didn't reply just have haha on it. We don't talk anymore but she posted a story saying no one was with her when she needed. 2 weeks passed. Now, what to do?

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Can someone tell me what's the case here? I would like to have her as my girlfriend
Can someone tell me what's the case here?
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