(((hugs))) to you and your poor little monkey
My ds also has multiple food allergies (dairy/egg/peanut/mustard) and though he had looser BMs when teething, they aren't green/mucousy like you describe. My first thought was the Hyland's teething tablets when you mentioned them. I never used them for Dylan simply because they are a lactose base, and lactose is by definition milk sugar
I would stop using the teething tablets like you've done, and give it a few days to see if his poops settle down.
FWIW, I used Camilia for Dylan's teething. It has pretty much the same active ingredients as the teething tablets, but in a water base. It's liquid, but comes in a box of 30 individual doses so is easy to give. Dylan had no problems with it at all. Got it at Walmart
HTH, and hope he's feeling better soon!