If this verse predicting Christ, why is it referring as just a Prophet then, not a Son of God or a Messiah? I thought it was revering to the Prophet Moses..
Well, if you read the words carefully, it is Moses announcing the coming of another prophet like him (i.e., like Moses). He would not have to announce himself, as he's already there.
I don't know enough about OT religious ideas, so I can't say why Moses referred to a prophet and not to "Son of God" or "Messiah", except that maybe they didn't or wouldn't have understood those terms. But this "Prophet" was evidently an important concept in their religion, at least at the time of Christ. In John 1.19-27, when priests and Levites were sent from Jerusalem to John the Baptist to ask him who he was, he first denies that he is the Christ; then they ask him if he's Elijah or if he's "the Prophet", which he also denies.
Based on the apostolic preaching (as I cited earlier), the tradition of the Church is that Moses was talking about Christ when he referred to a prophet like himself. And certainly, our Church regards Christ as priest, prophet, and king. There are many books, I'm sure, which deal with this, but the one that first comes to my mind is the first of the three volume series Jesus of Nazareth
by Pope Benedict XVI; he begins that book, if I'm not mistaken, with a treatment of the Deuteronomic passage in question and discusses its interpretation as a prophecy of Christ.