Doesn't sound like they are good with all the chicks.
I'd separate broodies with chicks. I've found that's best until chicks are about 3-4 weeks of age, then broodies are a bit more relaxed about letting other chicks and Mamas around one another.
It could be from pecking.
I'd clean the areas with saline or chlorhexidine, then apply triple antibiotic ointment.
Do you have 2 broody hens with chicks in the same area?