Hey Melissa!
WAR EAGLE!!!!!!!
My 2 yorkies have had conjunctivitis this fall, too. I dunno if it is the change of seasons or what, but their eyes have been itching them so bad and they squint them, and they rub their heads on the carpet, and their eyes have been oozing. I took just one of them to the vet (bc I didn't want to have to pay for TWO vet visits) and sure enough, it was conjunctivitis. The vet gave me this cream that I put in their eyes twice a day. It is a steroid and antibiotic cream. She told me to use it for 10 days straight, but their eyes cleared up completely after only using it a couple of times. So I just saved the cream and whenever their eyes start oozing, I squirt some cream in there.
Since your vet is closed, I would take him to another vet. It is not a serious problem and really any vet can give you this cream. I tried the Benadryl myself and it didn't seem to help, so if I were you, I would take him to another vet and get the cream and start using that.
GOOD LUCK! Hope your little ones gets well soon!