My cat's eye is doing something similar to others' cats, but his eye is swollen, red, puffy, leaking a yellow puss, and also seems to have bled at one point. I do not see a scratch of any sort, I just wonder if it is something allergenic. If not should I take him to the vet? I can't figure out what it is.

I would take him in to the vet. Even if it's an injury or an allergy, the vet would be able to tell exactly what it is and how to treat it. If it was bleeding, sounds more like a possible injury. Normally I'd watch something like that for a couple of days and see if it healed on its own, but around the eyes can end up causing more serious problems.