she keeps disappearing for like a month and then messaging me back
That in itself would be enough to stop me contacting her, no matter how much she says she misses you.
Think of how she has acted during your time together and also during the 3 years you've been apart. This is the way she is and without treatment she will stay this way, maybe even get worse.
Nothing wrong with wishing her a happy birthday but realise that it isn't going to change her one bit, even though I'm sure you're hoping for it to have some magical result and change her attitude towards you - we've all had that thought during our relationship with a BPD. It took me a long time to realise that nothing I did would change her.
If you still have feelings and want to be involved with her again - and it seems like you do - then be prepared for things to be exactly the same as they have been. Is this what you want?
Getting over a BPD relationship is very hard, but being in that endless and unpredictable cycle of conflict is even harder.
Good luck with whatever you decide to do.