Hen losing feathers; egg broke inside; sitting in nest - HELP!!!

Hi everyone. I am in desperate need of help. My BA (a little over a year old) is acting funny. I found her yesterday, sitting in her nesting box, not acting at all normal. I picked her up and discovered that a VERY thin, soft-shelled egg had broken inside her. I brought her inside, gave her a nice warm bath, and gently coaxed the remaining egg out from inside of her. She passed the yolk too. She immediately perked up. I even dried her off with a hair dryer (which she liked) before putting her back in her coop. I decided it was the best thing for her; she was alert and happy. Even ate some yogurt and drank some water for me.

OK. She seemed perfectly happy and alert again this morning. She perched last night and did her typical "cheering" when her "sister" hen laid her egg today (I have only 2 hens). I checked on her after work, and she was once again in her nesting box. Sitting on her "sister's" egg. Now I have noticed that she has lost ALL of the feathers on her breast. She is alert, but very ragged looking. Her feathers are haggard. Not at all the very pretty bird she was this summer. Not acting totally broody either though. She let me pick her up and gather the egg. Her tail is up.

If it was only the bald breast and haggard feathers I would think that she may have gone a bit broody; or even molting. But, these symptoms ALONG with the broken thin egg has got me all confused. I am relatively new to chickens - this is my first time raising them. I rasied her from a chick, so I am very attached to her. I would take her to a vet, but there are NO vets in my area able and willing to see a chicken. I even called a local farm, and they gave me the typical response - "She's only a chicken, just let nature take it's course."

Do molting or broody hens sometimes lay thin shelled eggs - or even have one break inside? I checked her vent and it looks pretty clean (and pink). I think I got it all, but there is some dry goop (possibly from yesterday). I got a much as I could. I am totally lost here...

PLEASE HELP!!!