Birth control refill is late, what do I do when it is finally filled?

So I took my very last pill yesterday, but the refill for my birth control hasn’t been processed yet. In fact, they’ve told me they won’t have it for another 4 days at LEAST. I take it for my periods (which I just got mine TODAY) and without it I’m worried I’m going to be in horrible pain, since that’s what happens every single time I’m not using it.

If it does come sooner than this, what do I do? Do I start taking it as soon as I get it? I do have an old pack from a few months prior that I had lost and then redound, would I be able to take some of the pills from that pack since they are all the same?