I have a compromised immne system. EVERY scratch I get, looks 'bad', and especially the cat scratches. My scratch will be red, puffy and 'angry-looking' for at least a day or two before the swelling goes down and then it heals fine.
I have found that neosporin or A&D ointment with bandaids will hasten the swelling reduction and healing process.
I would say if a scratch remains angry, swollen and very red after 2-3 days, it should certainly be seen by a Doctor. I would also venture to say, if a scratch were going to turn 'bad', you would certainly know before 2-3 days.