I don't know how to get calcium in her without causing further pain, and nor do I have any to hand. I think she'll be ok overnight and will be treated properly tomorrow.

There are a couple of BYC folk who really know their stuff and from them I learned to keep calcium citrate tablets in stock. Readily available as a human health supplement.
Some like Kris use Tums which are also for people for heartburn and are calcium carbonate. Those are fine but the citrate version gets absorbed faster and when a hen is egg bound that means she can use the calcium quicker.
In terms of giving them the pill I was surprised how easy it is. Just pull on their wattles so they open their beak and pop it in their mouth!
I know you are seeing the vet really soon but I wrote this so you have this info on hand.