Hi.
That's a hard one. Honesty usually works best, especially with friends. But you might want to think carefully about telling your current (or former) best friend that you've "had enough" of her.
For one thing, your feelings of annoyance may pass and you could regret pushing her away; if she's fallen out of your favor so suddenly, she might fall back in your favor! In any case, if you cared so much about her in the past, you probably don't want to see her hurt.
It occurs to me that maybe you've been spending too much time together--"connected at the hip" sounds pretty intense--and that seeing her even just a little bit less might make her less annoying.
You could even be getting closer to this new girl at the same time. You don't necessarily have to choose between the two of them, do you?
Of course, this might really be the end of your seven-month best-friendship. But even then, it's probably best to take it slowly and make sure you're being gentle and careful.
If you do try to phase out your friendship and she just doesn't get it, after a while you might want to tell her that you're trying to hang out with other people more or don't feel quite as close to her as you used to.