UPDATE: I wanted to provide an update for anyone who needs help with what we went through. As of today, our chicken is not only doing exceptionally well, but the prolapse is gone, she is laying regularly, is quite active and getting used to foraging outside again but still separated from our flock and sleeping in our home in a crate. I want to thank @Eggcessive for their help as well when we desperately needed it. Our Pumpkin is still under observation so this is not a guarantee in survival.
Day 1 - When we first noticed Pumpkin's prolapse, we immediately separated her from the flock, brought her in to review the problem and prepared a warm bath. After hours of seeing if she would pass the egg, and the prolapse unable to be replaced back in her, we evaluated the next steps. We removed Pumpkin's first egg surgically on our kitchen table after all options were exhausted. We do not under any circumstances recommend doing such a risky operation if a vet or experienced hand is available. The oviduct exit was not visible with the prolapse and she was becoming more agitated. The table was sterilized, Pumpkin was washed, and my husband wrapped her body and head in a towel and gently held her on the side while I incised the thinnest part of the membrane of the oviduct to remove a thin, sandpaper-like egg with a sterilized knife. A saline solution was prepared in advance to wash the wound. There was minimal bleeding as we did our best to avoid incising any blood vessels. We sterilized the wound and vent as best we could with the materials we had, and placed her immediately in a clean crate with water while she recovered overnight, hoping that she would be with us the next day.
Day 2-3 - Pumpkin survived the night. The prolapse was still present. Twice a day I continued with providing her a bath, morning and night, to keep the area clean and prevent further infection. I also limited her exposure to light but this in reality didn't seem to help us. The following day the egg bound prolapse reappeared when she was walking around our living room. She was trying to lay an egg. At this point I believe she wasn't going to make it, but I prepared the bath for her again and let her relax for about half an hour. I cleaned her prolapse and dabbed olive oil to keep it from drying before I placed her back in the crate. She laid the egg about an hour later.
Day 4 - The prolapse started developing a greenish-white, grey and black crust. I assumed this was necrosis, and I began a strict regime of preventing further infection. I was determined at this point to do everything I could for her. I went to my local pharmacy in Sweden and picked up the following:
-Calcium and D3 Tablets
-Klorohexidine Fresenius 2 mg/ml 1000 milliliter Bottle
-Medical Grade Honey
-Latex Gloves
-Cotton Pads
DAILY ROUTINE: Morning and night routine would include the following: a 30-minute Epsom salt bath with a drop or two of dish detergent. Pumpkin was submerged to the point that the prolapse was under water. With latex gloves on, I would GENTLY check the prolapse and remove as much of the urate buildup as I could, even if I was just agitating the water to loosen it. I did NOT force this, as the bath would do most of the work for me. During the bath, I would mix a crushed calcium tablet and mix it with plain greek yoghurt, a little sugar, and meal worms to help encourage her to eat it. I fed her with a little spoon while she was in the bath and she greatly enjoyed this.
After the bath, I would place her on a dry towel and pat her as dry as I could. No rubbing. I was careful where I was placing the towel and making sure the prolapse wasn't being handled. Once she wasn't dripping wet, I would prepare the next steps. New gloves are always put on for each step. I washed the wound and the prolapse/vent area with klorohexidine. During the first week, there was a little bit of blood on the cotton pads mixed with the white urates and some fecal matter. I blotted the crusted prolapse liberally with the klorohexidine, but made sure it wasn't soaked. Immediately after, I put on a fresh pair of gloves and applied medical grade honey. Not a thick blob, just a thin layer over everything, including the vent, around the vent, and on the prolapse itself. Finally, with a cotton pad, I applied olive oil to ensure nothing dried out. A new pair of gloves was put on for this step as well.
While Pumpkin was preening herself, I would go immediately and remove the dirty towel in her crate and replace with a fresh clean one. Clean water with a little apple cider vinegar was added to her bowl, and a small handful of food. She would be placed in the crate to rest and dry off while my husband started the fireplace to keep her warm (we live in a 300 year old cottage so we only have a fireplace for heat).
Day 5-6 - This process was repeated without fail twice a day. Pumpkin started laying normal eggs from this point onwards almost every day. By the end of Day 7, I noticed the necrotic crust that had developed was in fact a scab. I trimmed her feathers carefully around the area to keep it from getting further infected and this was a huge turning point, so I highly recommend trimming. This was the best case scenario for us as epithelialization (new tissue development) was clearly visible with bright red tissue under the scab. We made no attempts to remove or pick at this scab under any circumstances. Like clockwork, we continued our routine until a big part of the scab sloughed off in the epsom salt bath on Day 7.
Day 7 - A major part of the scab sloughed off today, and the prolapse was smaller on this day than ever before. We continued the critical care routine but once a day from here on out.
Day 8-11 - On day 10 the prolapse was completely gone. Critical care routine was continued once a day at night with excursions outside of the cage for half an hour to explore and stretch wings and legs.
Day 12 (TODAY) - Pumpkin is spending time outside now. We did not provide an Epsom salt bath today, instead she spent the majority of her time outside in the dust bath and foraging in our garden. If we notice a change in temperament or health condition, we will revert to a gentler routine of simply an Epsom salt bath, electrolytes, and observation indoors. I don't believe she is ready to return to the flock for a few weeks.