Glad that the eye is better.Update:
I have been gently squeezing the eye to remove pus and applying antiobiotic in the eye multiple times per day. The swelling has gone down a bit! I have ordered the antibiotics and they should be here within the next few days. No one else appears sick, and I have disinfected all of the hutches (with diluted germicidal bleach and veterinary grade hydrogen peroxide disinfectant). Im hoping all of these measures are enough to keep my birdies safe and healthy.
I worry about transfering it to my zebra finch. Will they become carriers and I will have to be careful of contamination for the rest of their lives?
Without knowing the cause of his symptoms, it's hard to know if it can be transferred to your Finch or not. Getting testing would let you know what disease you are dealing with.