I just looked back up at the photos, it apears she has cross beak. But I am sorry, I do not have the answer for you. I can’t really tell what it could be.
I don’t understand, what are the symptoms? When was her last egg (if shes a layer), can you show a picture of her poop? What is her behavior like?
You said she eats a lot, and then sits down with her head under her wing? Chickens sleep with their heads under their wings, so thats normal. How...