I would take him to a vet as soon as possible. Bostons always have a certain amount (very little) discharge, but what you're describing could be an infection, or a problem with his eyelashes, eyelid, or tear ducts, to name a few.
He has been on eukanuba for sensitive stomach for a while, however, we had to buy puppy formula of the same last time because they were out of the adult. He gets very few table scraps and one scrambled egg almost every day. He is three and a half. We also moved into a house recently which gives him more outside time. We live in Florida, so he lives in a very mild climate.