She has what's called a prolapsed vent. The oviduct can come out with the egg, and it's common in young pullets who aren't quite fully mature. This can be treated, but it is serious. First of all, attempt to get the broken egg shells out of her, as they will cause damage and possibly death! Wash your hands and get some fingers in there to work the stuff out. As soon as you are done with all that, coat the oviduct with KY jelly, petroleum jelly, or some mineral oil in a pinch. Slowly and gently attempt to work it back into her. Keep her separated from the other hens, as they will peck her to death. Keep a close eye on her to make sure she doesn't "pop out" again. Make sure she has a quiet place to stay, with access to water, but drastically reduced amounts of food to slow up egg production. Vitamins/electrolytes in the water are also a good idea. Best of luck, and keep us posted!