Unfortunately that looks like a lash egg, and that means she has salpingitis, which is inflammation of the oviduct. Sadly it can't really be treated, and all you can do is offer supportive care measures.
Her not laying and having a messy bottom is another sign that she has salpingitis.
You're doing great so far. Keep it up!
What breed is she? Age? When did she last lay an egg? Does she smell bad at all?
Her clear, white, green watery droppings the other day showed she wasn't eating enough. So make sure she keeps eating. Some scrambled eggs, meat, fish, or wet feed are good...