You weren't worried enough...
Yes the engine ran after the fire, and that fact was the reason that the fire did not continue to do damage, but it might have already done so.
Writers here have given lots of wisdom about how a carb fire could have started, and keeping cranking is the best way to get it out. BUT....
Once you are satified that the fire is out, and the engine is running smoothly, shut it down - you're not going flying. And forget about charging the battery with the engine, that's what chargers are for!
The carb contains a jet and a venturi (remember ground school?) The venturi in particular is a rather delecate metal part which can be damaged by fire. Such damage could result in it being deformed, and not providing proper fuel distribution, or worse, breaking off inside, and being drawn up into the induction system later in the flight. You'd be gliding then!
Once you know that there has been a carb fire, tag the aircraft not fit for flight until inspection. Only a disassembly and inspection of the carb can assure that it has not been damaged.
Were you to take the aircraft flying uninspected after the carb fire, and it quit because of carb damage, the resulting forced landing might not be entirely your fault, but you'd still be the guy who put it in! (And there'd be a lot more cost and delay than just the carb inspection)
For all of the chatter I've read on this forum about the rights of the the next pilot to fly an aircraft which has not been subjected to an unreported unusual event by the last pilot, the possible damage from a carb fire is right up there in dangerous things to not report, and have inspected.
I have disassembled Cessna 150 carbs (which are a little different for 152 carbs) and found that they were not safe for flight, because of carb fire damage. but the engine did still run.
Nice going asking, instead of telling us!
Pilot DAR