She told me that she's very disappointed and has been giving me the silent treatment.
This is validatable. She's dissapointed.
She also told me that she hates how her birthday is near christmas and how she doesn't like getting her birthday presents with her christmas presents.
This is... .but isn't. "Validate the valid; invalidate the invalid."
It's not up to you to "fix" her birthday. IMO, an end of January birthday is a stretch to tie it to Chirstmas, but those are her feelings, which she owns.
I've been thinking a lot about how an adult with BPD telegraphs their pasts as neglected children. It may be natural to try to "fix" this as children,.but since we weren't the neglecters, it's nit our job to make everything better. It's a very strong dynamic from which to detach.
Your boundary is set. She sounds like she is resentful that you want to celebrate her bd early. Can you accept that this is
her choice, and stick with your boundary?