In a C-172, on short final, with full load and full 40° flaps?
( With the asumption that carb heat went in at 200 ft AGL)
=> Go-Around
=> Throttle FULL => And KEEP your hand on the throttle to prevent kreep back.
=> Positive VVI => Lock Throttle
No problem to go from 40° directly to 30° (Most is drag anyway). Then Milk the flaps up => 30°, 20°, 10°, 0°
Most, if not all aircraft climb better with a clean wing => NO flap.
=> PoH
After a Go-AROUND desision has been been made? Throttle ALWAYS comes first. Flaps a distant second after positive VVI has been confirmed, then milk them up.
(And carb heat should already be OFF from your short final checklist.)