I would have her separated from the others and kept in a nice warm box with either a mirror or a stuffed animal.
Is her umbillicus okay? - Page 9
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I'm concerned about that spot on her head? Something is going on there. it's been a while and any gooy stuff should have come off by now, can you get a closer pic of what's happening on top of her head?
It's been a week and just looking at the previous pictures to what her beak looked like then from now to me it looks like its disintegrating. Or someone is peaking the heck out of it. Because she has lost some of it since the first pic, wonder if she got it caught on something..
Is she using the leg at all? after a week, she should be able to put some pressure on it, if not, please send some up dated pics need to see her joints again. Wonder if she has Slipped tendon, if so, she won't be able to walk. Have you been giving her Niacin? She should have gotten around 150ml per day that would have helped.
I wish you had someone who could take you to the feed store for some Save A chick[very inexpensive] or Poultry Nutri drench. and like @Lacrystol said could some of the other ducklings be messing with her. They tend to pick on one that isn't normal Or are you still keeping her separated but in the same brooder?
Looks to me the bottom part of the bill is growing normal and the top part isn't. How is she doing with eating? her leg doesn't look swollen but how does it look compared to the other one when you look at them are they both the same length when you put them straight? can you lay the one leg straight?