It certainly looks infected... maybe a wound, someone pecked her, or a bug or spider bite? I guess the point now would be to put her in a cage, separate her (however you must)... put her in an isolation place, clean, dry, fresh food and water, alone, quiet... And, start pumping Antibiotics into her... Baytril (I was able to find a generic one so it was a bit cheaper).... Penicillin... Tylan... get needles and syringes with the injectible antibiotics from the feed store... use the needles to extract the antibiotics from the bottle (whichever antibiotic you choose, one)... you can give it orally (without the needle), or give it into the breast muscle, injected.... go online to Jefferslivestock.com to search the antibiotics and read the manufacturer's info. and recommendations on them there... (if you want)... feed store personnel or owners are often knowledgeable and helpful with regard to what you should use, how much, for how long, etc...
She is a full grown hen (?), most have told me .5 (1/2) CC / ML ... the number of days depends on the antibiotic. You might also get a Betadine type cleanser and clean the area, clean the "wound" if there is one... avoid getting it into the eye.
If her eye is involved you can get the opthalmic oinment for that, for in the eye at the feed store also.
Be sure to watch and see if she is eating and drinking.
I am sure you can get better and more info by searching the forums here, or from others as they reply.
Best of luck.... I'm sorry she's so sick.
