How is her prolapse doing? Is it staying in? If she isn’t eating well, it might be better to not keep her in the dark.
In this thread, post 17 @casportpony says to give a minimum of 14 ml and a maximum of 23 ml per pound or weight, every 2-3 times a day...
Many vets probably would recommend putting her down with a lacerated or split open cloaca. Chickens sometimes recover from the worst possible wounds though. Any straining to poop or lay an egg, or struggling, could cause the prolapse to come out. Normally, you would keep putting it back inside...
Are the pictures above still containing the egg, or not including the egg? There is not a lot she can do for the tissue if it has split, other than trying to keep it clean with soaking and applying Vetericyn and plain Neosporin ointment often. It might heal if the prolapse is pushed back inside...
I am not an expert but it may be a prolapsed vent with egg binding. I would give her a human calcium tablet or Tums orally to help her muscle tone to lay the egg. Get her into a warm sink or pan of water to soak for 20 minutes. You will need to try and find the opening of the vent and try to get...