Photos of her cleaned up bum when you have time
Is she acting normal? How frozen was all that?
The soaking will hopefully help. After you have soaked her apply your ointment/cream.
Gently push on the prolapse to see if it will be go back. It may be too swollen to stay in. That's o.k., just keep the exposed tissue moist with your ointment.
She needs to stay hydrated, eat her normal food. You can give her a crushed up TUMS or 1/2tablet of Caltrate for extra Calcium. 1/4 of a banana is o.k. too
It doesn't look like the tissue is damaged, but more photos will be helpful. Is she bleeding?
Most of the time a prolapse can be fixed, it will take time and patience, so keeping her in would be good.