Near the lacrimal caruncle (the thing that eye discharge builds up at), it looks a little swollen near one eye compared to the other. It is very subtle, but definitely there and at the eye that he gets the most discharge at after sleep. Anyone else have experience with this? It isn't in the actual eye but right near the outside of it medially, so closer to the nose.

Sounds like the tear duct might be clogged. I would have the vet check it.