Is Harry the Horcrux?

The first half of the prophecy is:

“The one with the power to vanquish the Dark Lord approaches. born to those who have thrice defied him, born as the seventh month dies . and the Dark Lord will mark him as his equal, but he will have power the Dark Lord knows not”

The second half of the prophecy explains why Harry must die in book 7, so that Voldemort can be destroyed:

"and either must die at the hand of the other for neither can live while the other survives. the one with the power to vanquish the Dark Lord will be born as the seventh month dies."

“[N]either can live while the other survives.” On the face of it, the statement is absurd. Voldemort and Harry are both alive, and both survive, simultaneously. We tend to think of “live” and “survive” as synonyms. Yet if the two words are synonyms, the prophecy is incorrect.
Thus, as long as Harry survives, Voldemort is not mortal. Accordingly, Voldemort is, in a sense, not living. And perhaps, in some as-yet unknown way, Harry is immortal as long as Voldemort survives.

The reason that Harry must die in order that Voldemort may “live” (as a mortal) rather than “survive” (as a deathless immortal) is that the final Horcrux is contained within Harry himself.
But Voldemort’s death/Horcrux spell on baby Harry went terribly wrong, and blasted Voldemort’s body out of existence. Yet maybe Voldemort did, unbeknownst to himself, create that final Horcrux: in Harry Potter himself. The lightning bolt scar on Harry’s forehead is clearly more than a wound from the attack, since we know it magically links Harry and Voldemort. Could it also be the final Horcrux? And so for Voldemort to be destroyed with finality, Harry himself must die too.

Perhaps there’s some way to destroy only the Horcrux, without killing Harry. But from what we’ve seen so far, in order to destroy a Horcrux, such as the one contained in Tom Riddle’s diary, one must destroy the Horcrux-carrier too.