You say that she's acting like a brat..but I think she's got good reason to be mad at you. To be honest, I'd be finding your behaviour infuriating if I was your girlfriend. Telling someone that there's an issue but refusing to discuss it till later is rude. If you're not able to discuss the issue then and there, don't raise the issue in the first place.
Yes, I understand that you apologised for sending the "I'm done with you text" but an apology doesn't undo what you did. Combining the text with your current refusal to talk about things until you see her....yep, her behaviour makes perfect sense to me.
That's not to say that your concerns about the relationship aren't legitimate - I too would be pissed off if there was no acknowledgement of my birthday. But if you want to move forward, I think it's important that you also understand how your behaviour effects her. It's gotta work both ways.
Never regret anything that has happened in your life. It cannot be changed, forgotten or undone. So, take it as a lesson learned and move on.