When a Giant Frog swallows an enemy, is it able to move normally as long as it is not over-encumbered?
The rules regarding giant frogs say:
The frog makes one bite attack against a Small or smaller target it is grappling. If the attack hits, the target is swallowed, and the grapple ends.
The frog is no longer slowed down to half movement by the grappled creature (Player's Handbook, p195) once the creature is swallowed. So unless the creature's weight heavily encumbers the frog (if using the encumbrance variant), it can move normally. Remember, however:
The frog can have only one target swallowed at a time.
So it loses that option after it swallows a creature. Until the DM decides the target is no longer swallowed, anyway, likely via digestion.