If a vet is an option, then by all means, take them to the vet. If not, then you'll likely need to cut a slit in the skin to give the pus an exit.
Basic instructions (I am NOT a vet):
I've found disposable scalpels at my feed store. Get some disposable gloves as the infectious material is probably septic (and contagious to humans). Gather old, clean towels/rags. You'll need several.
Having a partner to help you hold the bird will be helpful, but if you don't have a buddy, then wrap the bird gently, yet firmly in a towel, with their head exposed. This will effectively bind the wings & feet without applying too much pressure on the respiratory system. Expect heavy bleeding when you cut the skin on the external eyelid. All facial wounds bleed like the dickens, so don't panic. The feed store likely sells a blood-stop powder too.
So, cut the lower eyelid open to give the pus a path of least resistance, and squeeze it like you would a cyst or blackhead, with firm yet gentle pressure under the pus pocket with the force directing it to the opening that you created.
Once you've got all the pus out, apply more blood-stop powder, avoiding the eye itself. House the bird alone, but within eye and ear-shot of its mates, you should be able to put them back in with their flock in a day or two. Monitor the healing, confirming that swelling is going down and doesn't appear to remain infected.
Keeping you and your feathered family in my prayers.
The little part within the eye that looks like pus is actually the other eyelid. I was trying for days to dig it out until I realized it was pink and moving back and forth over her eye! If there’s still pus, it must be way back in the corner of the eye.
