I'm not familiar with layer essentials, what is it, do you have a photo?
In the photo she has a messy bum, I assume that is from the eggs breaking inside her? You may want to wash her up if she's sticky. While you are doing that, inspect her for lice/mites and feel her abdomen for any bloat/swelling or fluid.
She was laying well until a change in feed. What was the change - from starter to layer or? What's the difference in protein content?
Getting a fecal float to rule out worms is always a good idea. She may be lacking in nutrition (protein?) if the layer feed is drastically lower than what she was eating. She may also have some type of reproductive disorder/malfunction. If she were mine, I would direct dose her with poultry vitamins for 2-3 days in a row, then once a week. Give her 1/2 tablet of calcium like Caltrate for 3-5 days too. Increase protein with egg, meat or fish.
The eggs were broken and you had to pull those out. So I'm going to assume the contents were spilled inside her too(?) I would worry about that causing infection, egg yolk/whites are a perfect growing medium for bacteria. Consulting your vet is always best, but again, if she were mine, then I would also give her a round of antibiotics. Do some research and figure out if that's something you want to do. If you sell eggs or you/your family are allergic to certain medications, then that needs to be considered as well.