Chicken Emergency

When we arrived home from church this morning I cut an apple up to give the the chickens. I noticed that Bella the bantam was not around to partake in the goody. I looked in the coop and she was there straining and bloody on her rear end. Upon closer inspection their appeared to be an egg stuck (bigger in size than what she should be laying). Three quarters of the egg was actually out but the shell was broken and hollow. I immediately started researching on the net how to get the remainder of the egg out. Proceeded to soak her in warm water with a little soap mixed in for lubrication. This actually did relax her and moisten the vent up for her to expel it. Her vent did look somewhat prolapsed after the egg was expelled. Not sure what it usually looks like immediately following laying an egg. I have separated her from the rest of the flock for a couple of days to let her heal. She does look a little peaked this evening and still moist on her rear end. This is Grace's favorite chicken, praying she doesn't get an infection and die. I think because our rooster is so much bigger than her she may need to be separated for life if she recovers so that the egg size can be a little smaller. If I didn't mention it before this was her very first egg to lay. Any sage advice is welcomed.