A: To refresh, the wording varies slightly on Move a Creeper, depending on what version/expansion it’s in, but all versions have you move a Creeper in play to “another player” or “any other player.”

and Creeper Reassignment says pretty much the same thing, but adds “If it’s currently attached to a Keeper, detach it before moving the Creeper. You must attach it to an appropriate Keeper (if possible) after moving it.”

In both of these cases “other” means someone other than the person who had the Creeper to begin with. So, yes, if your opponent is the only one with a Creeper, and it’s a two-player game, and you’re forced to play this card, then – sorry – the only player you can move it to is yourself. Sometimes Fluxx is like that.

Variations on Move a Creeper which have wording which doesn’t require this clarification include:
Anatomy Fluxx: It’s Contagious
Dog Fluxx: Bark It Away!