I have a question for you. Isn't Acts 2:38 still under the Old Covenant? I notice that everyone saved after Acts 2:38 was told to just believe. Acts 2:38 was intended for those Jews who were under the Old Covenant and it is the last we see of water baptism until the New Covenant begins.
The Old Covenant ended with Jesus' death on the cross (Colossians 2:13-14). Acts 2:38 takes place after Jesus' death. In fact, a portion of Peter's lesson, just prior to this, was to charge those present with having a hand in the death of Jesus.
Baptism is mentioned over eighty times in the New Testament. Acts 2:38 is the first time it is mentioned after Jesus' death, but it certainly is not the last time. See Notes on Examples of Conversion.