I don't think you should confront her, but I promise, you're not psycho. It's completely rational for you to be mad at your boyfriend for--and yeah, you're entirely correct in saying it--cheating on you.
That's what he's doing, plain and simple. He's betrayed your trust and done things that hurt you. Despite being in a monogamous relationship with you in which you are explicitly uncomfortable with him flirting with other girls, he continues to do so. That is a sign of major disrespect. While polyamorous relationships aren't bad, they only work if everyone involved is okay with it and trusts each other deeply. I may be assuming things here, but I'm guessing you just want it to be you two. He isn't respecting your boundaries.
Relationships are built on trust, communication, and respect. He's disrespecting you, betraying and ruining your trust, and isn't making a decent effort to communicate with you, seeing as he keeps feeding you the same lines over and over again.
The way I see it, cheating is a form of disrespect, and it's your boyfriend's problem, not yours, and not the other girl's. There's no "taking" someone from another person. She wouldn't be able to "steal" him from you unless it wasn't clear that he isn't really committed to staying with you.
He's disrespected you by continuing to do this even after you've caught him multiple times, deleting messages because he has something to hide, and is gaslighting you, which is another word for "trying to make it seem like you're just imagining things or like you're overreacting".
You're not. He's cheating on you. You get to be upset about this. Your feelings are valid. And unless you're prepared to continue this relationship, with him continuing to cheat on you, then it's for the best that you break up.