I won't even use the sugarcoating from her birthday cake to tell it how it is. You are in the wrong. Not her. If your character is too flimsy to wish her a happy birthday in person, at least try to be polite and simply ask her if she had a good birthday. Don't even bring up your woes that you weren't acknowledged. Just be a decent human being and be professional and friendly about it. Unless you're super close to your coworker...don't bother worrying about it.