Greetings
Wimomof2,
The chicken's eye is irritated. Brownish green stuff in not good. If the chicken has no upper respiratory symptoms, sneezing, coughing, discharge for the nostrils, etc. You'll have to investigate.
Wrap the chicken in a bath towel to restrain her.
You are exactly right...wet compress to loosen anything crusty. Then, gently open the eye, by pulling down the lower lid. Examine the eye as best as you can, look for blood spots or even cornea injury. Flush with sterile saline solution, to clean out any debris.
If you see injury, apply some Terramycin ophthalmic ointment, or a triple antibiotic ophthalmic ointment. Some keepers even use Neosporin triple antibiotic ointment (
without pain reliever). Do this twice daily, for 7-10 days.
If the eye looks clear, no injury or debris, then, check the ear hole by moving the ear feather tufts away. If you see anything oozing, crusty, or if the ear smells sour or foul, she could have an ear infection. Then, antibiotic ear drops will be needed 2-3 times a day, for 5 - 7 days.
Colloidal Silver is another good treatment for both the eyes and ears.
These are my thoughts on your chicken's closed eye. I hope I have been helpful.
God Bless
