Prolapse is when a hen's, how can I say this?, inner lining comes out, which is a real emergency. Other chickens will peck at it & she will die.
It can be treated with Preparation H, I have heard.
Sounds like your gal laid a shell-less egg. Some of the shell might be in there, however. Put on a glove, lube it up with vaseline or K-Y, & put your finger up there & feel around. Work any shell out of there until you don't feel any more. Then give her a quiet place to relax with lots of water & some foods rich in vitamins A, K & E , especially vit. A. She might have a nutrient deficiency, and vitamin A is one of the most important vitamins for a chickens overall health.
Some foods high in vit. A are: broccoli, butternut squash, carrots, sweet potatoes, pumpkin, mangoes & tomato juice. Spinach, peppers & alfalfa leaves for K, and sweet potatoes & broccoli for E, which helps boost the immune system.
If you have any of these veggies, boil them up until they are soft & chop them into bite-size pieces or mash them with a fork.
Also make sure she is eating her oyster shell, & try to supplement in calcium-rich foods. She also might not be getting enough vit. D.
What brand of feed do you use?