If all you have is one complete, unbreakable set, can you play a forced deal? The question is whether your own forced deal can be used on your own set, since the card just says: "Swap any property with another player. (Cannot be part of a full set.)"
The card text, as you quote, does indeed unambiguously prohibit trading away a card from your own full set, yes.
You might conjecture that this was not intended, but as it stands (with no errata or contrary ruling from an official source), card text prohibits the trade.
That said, Monopoly Deal is a lighter game, so I would certainly go with what feels right (obvious designer intent) over a strict adherence to card text. Just make sure that everyone at the table knows what the rule is and is happy with the change.