Good job! Nice photos too.
You may want to flush the eye and apply your ointment(s) for another couple of days to ensure all the gunk and infection is removed. Amazing what they can get in their eyes that can cause infection.
Here's another one from a few years ago that had a Foxtail in...
Have you personally done this?
I have to disagree.
Borax (laundry soap)is toxic to chickens. Perhaps you are thinking of Boric Acid which is found in some ophthalmic products, even at that Boric Acid should not be used in chickens.
A purchased saline solution can be used or if the OP desires...
Chicken pus is generally a semi-hard substance, it doesn't drain so you would need to physically remove it.
As for the Clindamycin, that would not be my first choice for treating respiratory disease infection, it's more suitable for joint, bone or deep wound infections. Tylan 50 or even...
It's hard to know, it may be behind a membrane(?) like this one was.
https://www.backyardchickens.com/threads/maran-pullet-with-swollen-closed-eye.1284967/#post-20846044