Your priest is correct that confession follows baptism. If you are being baptized this Easter Vigil, then you do not confess beforehand. This is because baptism is the gateway to the other sacraments and because baptism cleanses of original sin and forgives all sins committed by the person before his baptism. Confession is for the forgiveness of sins committed after baptism.
Your sponsors may be thinking of people who are received into the Church after baptism in another Christian tradition. These people do indeed go to confession before being received into the Church and are called candidates. Those who have not yet been baptized, such as you, are called catechumens. Candidates confess before reception into the Church; catechumens do not.
