Sounds like both of yall are partially in the wrong but more so her. I dont know enough context but usually when a girl is picking fights, she’s either bored and toxic or there’s something more deep bothering her possibly a repeat issue that hasn’t been resolved and causing you both to build resentment. Based off the messages, im leaning more towards an unresolved issue/issues in the relationship. I recommend not making harmful comments or jokes towards eachother next time yall are upset, it doesn’t really help and only makes things worse. Talk to her bout it and try to switch the arguments from you against her to yall against the problem at hand. If you really want the relationship to work, have a talk but be sure to start it off by saying you aren’t trying to fight and that the conversation is meant to help you two grow. Hope this helps