What Juells said about their friend's daughter pretty much described my 22 year old's teenage years, I'm afraid. And my daughter turned out to be an actual NPD. It's rarely diagnosed by clinicians, but as soon as she'd had one session with the psychologist she was sent to after (and if anyone doubts this bit, please feel free to search my threads on it from last year and the year before) she lied to the police in order to have me arrested, and they pushed for her to be assessed ASAP, they recognised traits in her which led to the near-immediate diagnosis. Whilst I'm obviously not saying that this is the case, or is going to be the case with your 13 year old, OP... please take it from someone who knows from bitter experience, that getting your child help if they need it at 13 is a hell of a lot easier than it becomes once they're an adult. And I wouldn't wish what my 13 year old son and I went through with/because of my daughter on anyone. She's rewritten history inside of her own mind to the extent that she simply denounces the truth unless it fits with her own narrative, she has no friends, her boyfriend is moving to the other end of the country (and yes; I do have a horrible suspicion it's to escape her, as he's had to call the police to stop her from hurting him once or twice), she's alienated her younger brother (who once adored her), and... I love her, but I really can't stand her. Because of what she's done to me. I look at her some days, when she's doing the whole "panic attack" breathing thing, or is screaming abuse at me (her latest is that I'm a "freak" and the old classic about no one liking me...!), and I find it difficult to reconcile who she is now with the baby I gave birth to and only ever asked that she be happy and healthy. My daughter is neither. And, sadly, may never be. If I'd known that there was help out there for her, when she was 13, I would have been knocking down doors... but I didn't know personality disorders even existed, actually, until she was 20. But now... she's trapped in a miserable existence, where she gets to be the permanent victim. And it's all her own doing, yes - but, as her mother, it does break me to witness it.
Hopefully your 13 year old is simply a hormone laden bratt... but she may not be. Talk to your GP. Describe her behaviour, the sudden shifts in mood, the walking on eggshells - and tell them that you're dreading future events, purely because you know she/her behaviour will ruin them, not just for you, but for others.