OP was doing their job. If you work in customer service of any kind, your job is to be friendly and personable. You can't just act unfriendly on the off chance someone is going to be rude and grumpy.

Yeah, maybe OP should have sung a few lines from the Beatles' "Birthday" to point out that they share a birthday. Maybe the woman you made the delivery to was having a rotten day otherwise, OP, or she's just a rotten person; it's still no call to be nasty to you. Hope the rest of your special day went well.

As a drama queen who's been in psychotherapy over it, I agree with your analysis :P. That is what we do. We don't mean anything we say. Drama queens hate themselves, so we put others down, and then cry about what a terrible person we've been for putting that poor person down -.-... Ah, well. Happy birthday, OP. Don't let her mean comment get to you :).

Most adults don't expect their entire birthday to be completely about them. Celebrate it, sure, but the world doesn't grind to a halt whenever you want it to.