I just had a 4 month old with something quite similar. Hers developed in he tear duct corner of her eye, upper second eyelid. Her's was smooth, round and could be moved around under the skin when you touched it. My husband is a retired eye doctor and he was pretty certain it was a tumor or cyst. I chose not to cull but observe. Bubble's 'growth' grew until it overshadowed about half of her eye. We didn't intervene other than to give her several doses of antibiotic and let nature take it's course.
It bothered her, she scratched it. It never opened but became raw more than once, then scabbed over. No pus in the drainage. Just clear eye watering. Suddenly, I noticed it was getting smaller. It took about 6 weeks but Bubbles's bubble slowly reabsorbed and now she is the picture of health with a completely normal eye.
Your chick looks like it has pus in the swelling. I would dose her with antibiotics, Tylan if nothing else is available for you to use and see what happens. I agree. You have something contagious in your flock. I would bet staph but without a culture you really won't know.
Definitely don't throw the baby out with the bath water. Also, if she will let you, apply warm packs soaked in Epsom salt water to her eye a few times during the day. If your other birds are recovering, this one should also. They are already exposed as mentioned so I would try to treat.
Bubbles is a spoiled little pullet. She got used to coming inside so 'Doctor Daddy' could check her eye for her. She knew she would always get a little bite of bread afterwards. Now she greets me every morning by flying up on my shoulder and looking for treats.
They are very resilient little animals. Don't give up on her.