Flirting can be okay. Hanging out with friends is just fine. But reneging on the invitation to your boyfriend and asking another guy? That is completely unacceptable in my books. Asking you to trust her would be considered normal if she was just going out with some friends to hang out. For something as major as a prom, there is NO reason for her not to take you. I'm guessing that her friends were planning on being there anyway, so she'd still have plenty of opportunities to talk and dance with them throughout the night anyway. Granted, I tend to over-analyze things at times, but I'd be extremely suspicious if my girlfriend did that to me.
She says to trust you, but trust is a two-way street. You two haven't been together all that long, so it's not as though absolute trust is reasonably expected at this stage. Yes, you need to trust her on some things, but she needs to make sure that she's not giving you reasons to doubt that trust. And this move of hers isn't helping that trust one little bit.
I think you two need to talk.