I had this exact thing happen. She's more than egg bound, she's prolapsed.
First thing I did was coat the area with veg oil to keep the membranes moist, if they dry out, the skin will die and she'd be open to gangrene. Then I tried to push the egg back inside her (gently) to try to find the right "hole" to exit from, but this didn't work.
I ended up having to operate. I sanitized a razor blade, needle and thread and I opened the skin surrounding the egg (it was easy to avoid the blood vessels) and removed the egg. Acting quickly, because the membrane wanted to disappear back in her vent, I sewed the incision closed and she pulled the skin back inside. I kept her in a darkened crate for a few days for her to heal (the dark will help her not to lay eggs.) She dripped a little blood for a day, but was otherwise acting normal.
I watched for for a while. There's no cure for prolapse, so I knew if she did it again, she'd have to be culled. Oddly enough, my hen never did it again. She continued to lay eggs and live a normal life.