I'd reccomend you put her in a small room (bathroom, large closet etc...) or a large dog crate.
Leaving her in a small carrier with no litter box may make her hold her urine causing an infection. It may also teach her not to use a box altogether.

As soon as she is steady on her feet I'd move her into a larger room & keep her there for a bit. If she is in pain she should know enough to be calm.

Did you ever find out if the shelter will reimburse you?

Good luck. I hope she has a safe & speedy recovery.