Infection or Eyeworn
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It may take tweezers or a manicure tool and cotton to get the yellow pus out since it tends to harden. Sulfadimethoxine or Sulmet is used to treat symptoms of coryza, and Tylan can be used along with it to help prevent secondary infections, such as air sacculitis. Many people choose to cull chickens with coryza, since that disease tends to be chronic and chickens are carriers for life. Of course, that is a personal choice. Testing can confirm what it is, or you can get a necropsy done by the state vet to confirm it. Sorry that you are dealing with this.
Welcome to BYC! That sort of pus is hard to get out and like Eggcessive said, might be best to use tweezers and/or a manicure tool.
Before you cull her, if that's what you decide, try squeezing it like you would with a big pimple and that might be enough to pop it out.
You might also want to look at this link:
Warning - graphic pictures there!
FWIW, I had a chick with something like that. It was happy and healthy in all other ways, but I treated him with antibiotics anyway... Zero change. Then I did the pimple thing and out came the blob. Being the way I am I had to cut it of and in the middle of it was a foreign body. So I guess his immune system reacted by encapsulated it with the pus. I guess what I'm trying to say is that not all these eye problems are respiratory disease, so it's definitely worth trying to get it out.