You did a good job getting the egg out. The tissue is thin and can tear so don't feel bad. I would have expected it to tear and bleed some, so you did a very good job!
She's exhausted, so I wouldn't soak her again since it already stresses her.
If she gets soiled just rinse the prolapse off or spray it off with clean water or soapy water, then rinse. Keep your water on the cool/room temperature level instead of it being hot when you rinse her.
She needs the Calcium so get that into her. Pull down on her wattles to open the beak, put the tablet right into the beak, let the wattles go and let her swallow. If you want to, cut the pill in 1/2 and give her a piece at a time.
Then work on hydration. Sugar water is good to give. 1tsp sugar, a pinch of salt, a pinch of baking soda to 1 cup water.
Pooping is good!!!!
Now, she may actually have another egg on the way or a soft shelled egg. So don't freak out. Just be aware of it.
Keep the tissue covered with your ointment or oil, whatever you have.
Let her rest, but push fluids if you can and get the calcium into her.
In the morning, offer her a little wet mushy feed.