Should I delete my cousin who keeps commenting on my FB Wall & photos?

like whenever I post up a new photo she'll be one of the first to comment on them. Once I made a status that said " dammit! Who ever stole my ******* basketball shoes is gonna get thier *** kicked!" then a few sec later she commented and said "you need to watch your mouth". I was so heated at that time I was gonna tell her to hop off my ****** page. I put petersburg,Va as my hometown because I was raised there for most of my life so I rep. petersburg but I was actually born in DC. Then she tried to call me out and posted that I was not from petersburg on my wall. Like wtf? you're making me look phony by saying that in public. I don't know why she's doing this we're not even really close anymore she's just an older adult cousin.