Although the hen you're showing seems to be prolapsed (or well on the way to it) we'll need more information:
Exactly what are you feeding them? Hopefully chick starter medicated with amprolium. How is your brooder set up? Are they all eating and drinking, for sure? You've seen each one of them do so?
What are their droppings like?
After shipping or moving, babies are apt to do this. That's why it's a good idea to start them on probiotics on the first week. (I use plain yogurt) to help the good bacteria get established (better) in their digestive tract. That's for healthy chickens.
At this point, your birds are experiencing something else. Can you tell us what you consider a healthy dropping ( just so we can make sure we're on the same page) and what their bedding is please?
For the probiotics (until we can get more information) use a dab of yogurt per chick. personally I like to mix it with their starter crumbles, a little boiled egg yolk (mushed up), a little water, and a teaspoon of yogurt. Mix this til slightly moist but not sopping wet - poke at it to get them to eat it. The live bacteria in plain yogurt help inject the gut with good bacteria to help them get through the stress of their first few weeks. (Use it weekly at least).
Until we hear from you, i wouldn't treat them with anything. You might pick up a thing of Sulmet or Corid from the feedstore if you're by there before we answer back. Just don't give it yet - it might not be necessary if the probiotics help jump start them back into health.
On this bird, you should have her separated or those other chicks will peck her vent right out. She should have the same brooder conditions as they all do at week one. You can use blu-cote on the bleeding. If you get her digestive tract back in order, the inflammation causing her vent to protrude should improve.
Honestly, every time I've bought feedstore chickens that were just shipped, I see this in at least one chick. Usually two or three days of probiotics fix it right up as long as they're on good medicated food and all other conditions are good. The trick is keeping the others from picking it.
You might also try using a red light in your brooder - not for heat, but above them to make all things in the room red. That way nothing looks especially red and thus especially pickable. I'd do this if you can't separate her. You can get red bulbs at most stores, like
Walmart. Red bulb, not UV heating lamp.
