Eye worm would probably not be the case in Alaska, since it is normally found in warm tropical climates where the Surinam cockroach is found. More than likely it is a symptom of a respiratory disease such as mycoplasma (MG,) or coryza. Does she smell bad around her face? A peck injury also could be possible, especially if you see any marks. Does she have any other symptoms such as watery or foamy eyes, nasal drainage, or any sneeze or cough? If you have any eye wash or Neosporin ointment, you can put some in her eye twice a day. Antibiotics such as Tylan 50 and oxytetracycline can be used to treat respiratory diseases, but these diseases are easily spread to other chickens, and make carriers of your flock. Here is a link to read about MG and coryza: http://edis.ifas.ufl.edu/ps044
Eye worm is treated by giving Valbazen mixed with water and instilled into the eye. Then give Valbazen 1/2 ml orally, and repeat in 10 days. You should be able to see eye worm in the eye--they are 1/8 inch long.