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This is correct. Neosporin with pain reliever is safe to use on chickens because the pain reliever is a completely different type of drug, a distant relative of morphine. There's other antibiotic ointments (Bacitracin maybe?) that use cetacaine or a similar "caine" drug that you don't want to use. The reason is that chickens are very sensitive to them; the therapeutic (effective) dose is very close to the lethal dose for them.
First aid is similar to people -- try to clean the wound with whatever you use, plain mild soapy water, dilute Betadine or peroxide, a wound cleanser (check label for "caine" drugs though -- whatever. Then an antibiotic ointment. She might let you place her in a warm bath -- dishpan, sink -- and relax so you can at least rinse off the wound then get some ointment on it. A dressing is often not practical, although you can lay some gauze there and tape it on with duct tape on the feathers if there is a real need, like she picks at it. You have to let the duct tape fall off on its own. Or wrap around with gauze or vet wrap. Best to keep her indoors for a couple of reasons. Flies will lay eggs in the wound and you could get maggots in the wound if outdoors, which can be lethal in themselves. Also, the other chickens will peck at any open wound. For pain, the antibiotic ointment itself will help a lot. Sometimes people give a baby aspirin once or twice a day; I don't know how effective this is, if at all.
Culling is another option, and it's your choice here, of course. If they won't eat or drink, there is not much you can do, but since she is, she does have a reasonable chance of recovering.
Wounds do heal even with the skin gone, yes. They form scar tissue from the edges into the center, again much like people. Takes a little longer, of course.
Chickens do heal remarkably well, as someone said, especially if she will eat and drink for you; I sure hope so, and hope there is not a lung injury (the wound doesn't sound like it is in the right place to have affected her lungs.) Good luck!