Mystery illness? Please help!

[Anabariful]

I have a 5/6 month old Lavender Cuckoo Orpington hen who is with 3 other Orpington hens and a Orpington rooster. Everyone was and is doing great until a few days ago I noticed the Lavender hen has been hiding out in the barn quite a bit. :/ Today I picked her up and her weight seems okay but she has white droppings all over her back side. I did see her go in the nesting box for about 10-20 minutes then got out. I have never seen her or any of the other hens lay an egg yet as they are still kinda young. I have seen the rooster start mounting them this past week. Is she egg bound possibly? She doesn't have any other symptoms. No cough, no sneeze, no limping, no blood. Just hiding out in the barn, laying down, with liquid white stools. Any help?

 

[Anabariful]

My apologies for the crass close up of her bum I just happened to catch the photo of her releasing stool and her entire vent prolapsed when doing so. Is this just a prolapsed vent or stuck egg?

 

[Anabariful]

 

[Anabariful]

Went back into the barn and found this egg with her. It appears to have blood on the shell as if it was stuck? I'm assuming this is her first ever laid egg. Anything I should do to treat her?

 

[Anabariful]

 

[Anabariful]

Also, we're in the dog days of summer so high 70's-low 90's is the norm. Liquid white stools from the excessive water drinking due to heat? After she laid her egg, she then went back to the nesting box to rest. I caught her sleeping. I'm assuming the stuck egg was a very traumatic experience for her.

 

[Anabariful]

Went back to check a third time and no improvement. She's still in the box, facing the wall, heavily breathing, laying down. I have bowls of food and water near her and she hasn't touched them. I did clean off her bottom and clip the dirty feathers. Any help?? Anyone??

 

[Anabariful]

I also checked for an additional stuck egg and there isn't any.