Coincidentally, those are the exact symptoms I've been treating for the past week in an EE hen of mine, right down to the not eating or drinking.
It began as pink eye, which is basically an eye infection. So I treated the eye with antibiotic eye drops. Next day, the eye was swollen shut and a white film had replaced the pink film. No other discharge or symptoms of CRDs (respiratory disease), but the tissue around the eye was puffy.
I went to the feed store and found some teramycin eye ointment, a tube smaller than my little finger for $30. It did no good, but I kept it up. Meanwhile, I decided to order some Tylan 50 from this place
https://pet-healthcare.revivalanimal.com/search?w=Tylan 50 which came within just a couple days, so I treated her with it for five days twice a day.
During this time she refused to eat or drink, so I tube fed her to keep her strength up so her immune system would function, and she has very slowly regained her will to live, although she isn't eating enough. I still need to tube feed her once a day. (Not hard to do.)
The eye is all but blind. The white film has become so thick, I can barely make out her eye behind it. But she is no longer lethargic and is starting to eat and drink little by little. The swelling has gone away, but she prefers to keep the eye closed. She never had any discharge or sneezing or coughing or trouble breathing. I still have no idea what it is that made her so sick. No other chickens in the flock of 22 have any of these symptoms.
Perhaps my experience with my hen will give you something to go on. I did start a thread on this topic, but none of the people here who know a lot about chicken diseases were able to figure it out either.
Hopefully, your hen can recover as it appears mine is. I suggest you rinse the eye each morning with saline or people lubricating eye drops, wiping the crust away with a Q-tip or cotton ball, then apply the eye ointment. This will give you information on how to tube feed.
https://www.backyardchickens.com/th...d-pics-for-visuals-very-detailed-post.805615/