Why do you think she has an egg stuck in her? Can you see it when you look at her vent?
Soak her bottom in a nice warm bath to relax her & her muscles for a while.
Put on a vinyl/rubber glove, lube it up with some KY or vaseline and try sticking your finger gently up her vent. Do you feel an egg? If so, try to lube it up as much as you can, and do her vent as well. Then put her in a quiet, dark place for a while & let her try to pass it. 
After she passes the egg, leave her in a dark area for a few days to recover from her experience & heal up. The darkness will slow the egg production/formation. You should try to feed her some foods that are high in vitamins A, K & E , especially vit. A. She might get a nutrient deficiency caused by all of the stress, 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.
Also cook her up a hard boiled egg for some extra protein.