Thank god! I asked the vet at work to look at him, and it's not a spiderbite. It turns out he either chewed on his foot and made it raw, or stepped on something, and the broken skin was just too inviting to the horrible staph germs that are all around our grody apartment building. So they cleaned and drained his foot and he's on puppy antibiotics now, so hopefully the infection will clear up soon.
So, while he's still not feeling great, it's not as bad as we thought! (And it was cheaper to fix, too, thank god)