there is nothing unusual about magicaly fast recoveries in the world of tv. I wouldn't worry too much about how fast carl was up and about.
Glen Mazara has gone out of his way several times in interviews to tell the viewing audience that they want the show to be a realistic as possible on how people today would deal with a fictional zombie apocalypse which of course must be a metaphor for how us humans may deal with a huge natural disaster that wipes out the majority of the population.
So, why would he tell fans he wants it to be as realistic as possible and then not try to come up with logical explanations for inconsistencies in the dialog?
well one explanation is they are too busy producing the show to be nitpicking the dialogue the way we are. And likely they are modifying things as they go so what they thought was going to happen in one episode doesn't necessarily really happen. Also, he likely was talking about the big story lines and direction of the show when he said he wanted it to be realistic, not the day to day time line.