I agree it's lice.
You mention she's sick -symptoms? I do see the eye issue with some bubbles/pus, does she have other symptoms like coughing, sneezing, wheezing, mucous, anything inside her beak like mucous or lesions?
Is she laying eggs?
Pooping?
Have you introduced any new birds within the last 30 days?
I also agree to dust her with a Permethrin based poultry dust. Treat the coop/housing with Permethrin spray. Probably wouldn't hurt to dust your other hens as well though often only a sick bird is more prone to having external parasites since they feel poorly, but at least look your other hens over for bugs.
The eye, I would flush with saline, remove any pus/bubbles, etc., then apply an eye ointment like Terramycin or if you can't get that, use Original Neosporin (or compatible store brand). Do this at least once a day, but twice is usually best.