Have you give her a good check over for any mites or lice?
I would put a little plain flour on the sore bits if they are still bleeding, then cover them in sudocreme
They sound like red mite - they are very tiny, usually grey/black but are red after feeding
They are horrid little things and so so difficult to get rid of.
If you could, I would move mama and chicks out of the coop for a few hours, clear the whole thing out, spray and scrub everywhere, then mix some DE with a little water to make a thick paste and paint it in all the nooks and crannies, especially the perch ends, then powder every where and let it air out. You can also order "redmite kits" online which have a smoke bomb in them, they are meant to be pretty effective against redmite.
I find with skittish hens it's best to catch them at dusk, once they've gone into the coop, they're more docile - it should be easier to dust her then.
Saying that, I've never raised chicks so it might be a good idea to wait for someone to make sure this is all safe for young birds