Usually they have either lice or mites, but I don’t think both. I may be wrong, but I did read an article about them not co-existing. Lice eggs looked like they were in her feathers in the picture. Anyway, permethrin 10 spray or garden dust, both work well on either. If you use one at 7 day intervals about 3 times, you should be able to control them. Of course the coop, roosts, and nests need treating as well, and a bedding change. This is what I use @38 ml per gallon below.
Are you using NutriDrench or Poultry Cell? I was going to suggest using a vitamin and mineral supplement in her food or water, since her skin issues could be related to a difficiency if it is not just the lice.
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