Should I put this cat to sleep? Anyone know anything about cat illnesses?

There was a young cat who I was feeding outside. He's only been around a couple weeks. I noticed some severe nasal congestion so I put him in a cage in the garage for the night. In the morning I saw he had diahrea. The vet tested for FIV and FLK and he was negative. Then the vet sent me home with revolution and Clavamox, but no real diagnosis. He said his intestinal tract was "inflammed" and his lungs were "seriously congested". I have work travel coming up next weekend, and this cat is seriously sick. His nose looks kind of raw. So far I've given him 4 doses of Clavamox (2 days worth) and he still sounds like pneumonia. He still has the runs and it's dried into his coat around his legs. I'm considering taking him to ASPCA and having him put down. I try so hard to save these guys, but I'm wondering if this is realistic. I've got 4 indoor cats, and without knowing what he's got, I'm afraid something will get to them. Any ideas on what he has? Should I put him to sleep?