She may have conjunctivitis, which could be from pecking around her eye, mycoplasma (MG,) or from an eye infection. Does the white look like tissue, pus, or her third eyelid? I would apply a warm wet wash cloth soak to her eye while holding her in your lap for about 5-10 minutes, to soak off the crusty drainage. If you can get Terramycin eye ointment or Vetericyn eye gel from a feed store, that might help. You usually have to ask a clerk for those. But saline can be used to clean any gunk out of the eye, and QTips can be used. Have you seen any sneezing or nasal drainage from her? If you think she could have MG, Tylan 50 injectable can be used to treat that. Dosage is 1 ml for a 5 pound chicken 2-3 times a day, and it can be given orally or as a shot. Here is a bit of reading about MG:
Mycoplasma gallisepticum
Synonyms: MG, chronic respiratory disease (CRD), infectious sinusitis, mycoplasmosis
Species affected: chickens, turkeys, pigeons, ducks, peafowl, and passerine birds.
Clinical signs: Clinical symptoms vary slightly between species. Infected adult chickens may show no outward signs if infection is uncomplicated. However, sticky, serous exudate from nostrils, foamy exudate in eyes, and swollen sinuses can occur, especially in broilers. The air sacs may become infected. Infected birds can develop respiratory rales and sneeze. Affected birds are often stunted and unthrifty (see Table 1).
There are two forms of this disease in the turkey. With the "upper form" the birds have watery eyes and nostrils, the infraorbitals (just below the eye) become swollen, and the exudate becomes caseous and firm. The birds have respiratory rales and show unthriftiness.
With the "lower form", infected turkeys develop airsacculitis. As with chickens, birds can show no outward signs if the infection is uncomplicated. Thus, the condition may go unnoticed until the birds are slaughtered and the typical legions are seen. Birds with airsacculitis are condemned.
MG in chicken embryos can cause dwarfing, airsacculitis, and death.
Transmission: MG can be spread to offspring through the egg. Most commercial breeding flocks, however, are MG-free. Introduction of infected replacement birds can introduce the disease to MG-negative flocks. MG can also be spread by using MG-contaminated equipment.
Treatment: Outbreaks of MG can be controlled with the use of antibiotics. Erythromycin, tylosin, spectinomycin, and lincomycin all exhibit anti-mycoplasma activity and have given good results. Administration of most of these antibiotics can be by feed, water or injection. These are effective in reducing clinical disease. However, birds remain carriers for life.