You raise the much-debated topic of the identity and self-awareness of Jesus. The Gospels do not provide specific information about this. Matthew and Luke report that Mary and Joseph knew of the unique identity of Jesus from the time of his birth (Matthew 1:20-25; Luke 1:26-35) but say nothing about whether they told Jesus what they knew. Of course, if the content of the birth stories is reliable at all, it seems likely his parents would have discussed with him a matter of such significance. Further, the story of the 12-year-old Jesus at the Temple suggests that he had a deep sense of his unique relationship with God from childhood. He tells his earthly parents, who seemed to have had a lapse in understanding: "Did you not know that I must be in my Father's house?" (Luke 2:49). Jesus' self-awareness no doubt deepened as he "increased in wisdom and in stature" (Luke 1:52). His baptism certainly presupposes a profound consciousness of who he was and what he was to do.
At a scholarly level, the discussion of the identity of Jesus is extremely complicated and controverted. It involves understanding the nature of the Gospel narratives, seeing the ministry of Jesus in the context of Jewish life, as well as understanding how Jesus was seen by the early Christians, who had experienced him as risen Lord. Space does not permit treatment of all the conflicting scholarly views on who Jesus was--prophet, holy man, miracle worker, sage, social or political reformer, or "Lord and God," as Thomas confessed him after the resurrection (John 20:28). You can survey some of these views by following the discussion on Beliefnet. Or you can read helpful books such as Ben Witherington's "The Jesus Quest" (1997) or one of the popular books by N.T. Wright, such as "Who Was Jesus?" (1992), "The Original Jesus" (1996), and The Challenge of Jesus" (1999).
My own position, which is closest to that of N.T. Wright, is that the extraordinary impact of Jesus' life, the remarkable rise of Christianity, and the witness of the New Testament, require that we do justice both to the "human" as well as the "divine" aspects of the mystery of Christ. Because Jesus was fully human, we must affirm that he, as well as Mary and other followers, experienced a progressive understanding of who he was. In the Jewish context, titles such as "Messiah," "Son of God," and "divine" could apply to anyone who was sent by God and spoke and acted with the authority and power of God. It was only with the decisive events of Jesus' resurrection and the gift of the Spirit that full knowledge of Jesus' intimacy with God and his sharing of God's glory as divine Lord were revealed. It was the experience of the resurrection and the outpouring of the Spirit that led the early Christians to worship Jesus and proclaim him as Lord and God. In turn, the Gospel and the worship of Jesus served as the critical bases for later theologians to formulate the teaching of the Holy Trinity--one God revealed in three persons, distinct but united and dwelling in each other--the fullest doctrinal explanation of the mystery of Christ.