Sorry, I can’t help with egg issues. Do you have a picture of the egg on her feathers and her butt?
Maybe one of the med cracks @Wyorp Rock or @Eggcessive, can help?
It happens more often a chicken is not allowed to roost with the flock. My Janice was bullied when she was a young pullet without brothers or sisters.
She preferred to sleep in one of the nestboxes as far away from the others as possible. I put her on the roost with the others every evening...