Skin problem on chick

[Bird in a Birch]

Does anyone know what might be wrong with this chick’s skin? It fell into its water dish at one day old. I found it that way on its back peeping its head off. I dried it off and put it under its mom for the night. The next morning my husband saw the mom try to kill it. We took it away and treated the gashes along each side of its face but noticed it was also limping. The skin on the knee? under the left wing is rough and thick and has no feathers. Don’t know if it was always like that and if the leg issue is why it fell in the water.