Not a lot of time passed, but more than a day. My guess was a week. Yes, an improbably amount of time to heal from a gunshot, but this is television we're talking about.
I've been impressed with how realistic the show had tried to stay to what may be likely situations in a real zombie apolocopyse. Why would be they bungle it now?
But agreed - a week + is likely between Carl's surgery and seemingly full recovery.