My new, 10 week old kitten has goopy, red, swollen eyes...?

I got my kitten on Sunday and he was 100% fine. On Monday morning I woke up and one of his eyes was really red and kind of swollen. By the time I got home from work, one eye was sealed shut and the other has tons of goopy stuff in it. I was going to take him to the vet last night but I decided to see if using warm water and a washcloth would help any first. So I've been wiping his eyes with a clean, warm washcloth and they look better for about 20 minutes then they get all goopy again. I wasn't home for about 2 hours last night and I had wiped his eyes before I left and they were fine. By the time I got home it was sealed shut again. I didn't wipe them at all throughout the night and this morning one is really read and they are still pretty goopy, but nothing compared to last night. Does anyone have any idea what this could be? I was thinking URI but he isn't showing any signs of having a cold.. no sneezing, running nose, etc.