Am I in the wrong?

In this story there is me, and 2 other girls. Call one A and one T

So me and T were staying at A’s house for her birthday on a Friday night. We were all best friends and had all classes together. The Saturday morning T was showing A messages between her and her sister. A told me that she saw a message that said ‘ can you block A and me from seeing your story because when I lied to them about why I can’t do something, your story always catches me out’ and when A told me this T had already gone home because she didn’t want to ruin her birthday. When I found out I messaged T and asked her nicely and T started getting angry and said that if she does tell the truth me and A will get angry at her. Eg- she lied about why she couldn’t come out with us incase we got mad at her. We told her we never have gotten mad at you for not coming out because we know that people don’t always have the money or they just can’t be bothered coming out.

This kept carrying on and T started playing the victim and making out like me and A were bad people who would always get angry at her, which isn’t the case. And then we started questioning why she would lie about other things which we had noticed she had lied about in the past but didn’t say anything.

Now it’s Monday evening and me and A didn’t speak to T at school today and we don’t really plan on doing either. T has been saying to other people that we are in the wrong and had a go at her for no reason and said she tried to message us to sort it out which she didn’t.

Now it’s getting to the point where so many other people are getting involved and questioning me and A because T told them that we were in the wrong.

Were we right to stop speaking to T for being a pathological liar?

* in this story i left out other lies T told because it was things that didn’t cause the argument but still happened*