Matthew 11:2-3, When did John the Baptist learn Jesus was the Messiah?

When John heard in prison what Christ was doing, he sent his disciples to ask him, "Are you the one who was to come, or should we expect someone else?"

//In trying to figure out how and when John learned of Jesus' Messiahship, we have on record two primary events: Jesus' baptism, and John's imprisonment. Let's start with the latter. Today's verse, in Matthew, indicates that John, sitting in prison, had not yet heard of the Messiah's arrival. However, John 1:29 reads differently:

The next day John saw Jesus coming toward him and said, "Look, the Lamb of God, who takes away the sin of the world!"

But two chapters later in John 3:24 makes it clear that "This was before John was put in prison." So John's Gospel insists the Baptist knew about Jesus before prison, while Matthew says he learned about him only after being imprisoned. But wait. It gets even more complicated. Reading now about Jesus' baptism:

Matthew 3:13-14, Then Jesus came from Galilee to the Jordan to be baptized by John. But John tried to deter him, saying, "I need to be baptized by you, and do you come to me?"

Doesn't this seem to indicate that the Baptizer knew about Jesus before baptizing him? That's Matthew's version. If we read the story in John's Gospel, we get a different story:

John 1:31-33, "I myself did not know [Jesus], but the reason I came baptizing with water was that he might be revealed to Israel." Then John gave this testimony: "I saw the Spirit come down from heaven as a dove and remain on him. I would not have known him, except that the one who sent me to baptize with water told me, 'The man on whom you see the Spirit come down and remain is he who will baptize with the Holy Spirit.'"

Clearly, in this version, the Baptist didn't know about Jesus until after he had baptized him.

Oh, what a tangled web. If we must choose between Matthew and John, John's story at least makes chronological sense.