While you are awaiting some more advice, you can start by drawing up a warm bath for your chicken. The water can be about 4 inches deep. A dish pan or kitty litter pan works well for this. Once you stand her in the water, gently push down on her back. She should settle in nicely and rest. This will help gently clean off all the gunk so you can get a better look. Once she is clean, take some new photos and upload them here. The bath will help her relax too, this clearly can't be comfortable.
