I can go all the way back to the beginning if that helps. Throughout salvation history, God has consistently sought to extract a confession from man. For example, in the beginning, we read "Who told you that you were naked?" Or, "Where is your brother Abel?" I could go on and on throughout the pages of Scripture.
These were all
types which culminates when God actually enters into his creation by becoming Man in the person of Jesus Christ. After His death and resurrection, on the evening of Easter, our Blessed Lord appeared to the Apostles and breathes on them. (This is significant itself given it is only the second time in Scripture where God literally breathes onto man - the first being when He breathed life into Adam.) When Jesus breathes on them, He imparts on them the Holy Ghost,
and then gives them the authority to forgive sins. St. John records the event as follows...
"On the evening of that day, the first day of the week, the doors being locked where the disciples were for fear of the Jews, Jesus came and stood among them and said to them, 'Peace be with you.' When he had said this, he showed them his hands and his side. Then the disciples were glad when they saw the Lord. Jesus said to them again, 'Peace be with you. As the Father has sent me, even so I am sending you.' And when he had said this,
he breathed on them and said to them, 'Receive the Holy Spirit.
If you forgive the sins of any, they are forgiven them; if you withhold forgiveness from any, it is withheld.'” (John 20:19-23)
This is where the Christian practice of confession became a sacrament. In order for the Apostles (and their successors) to be able to forgive sins,
they must first be told the sins. Hence confession, by definition, must be auricular. It has been this way from the beginning of the Church. We see this in practice in Acts when the Ephesians confess their sins to Paul in Acts 19:18. You mentioned St. Paul's epistle to the Corinthians, and to the faithful there the Apostle tells them he is charged with the "ministry of reconciliation." ( 2 Col 5:18) St. James instructs the faithful to make a confession (5:16) and St. John tells us if we confess our sins, they will be forgiven. (1 John 1:9)
Confession is practiced immediately from the Church's infancy, as testified to in the Scriptures and then in each subsequent century. (i.e. the Didache, St. Irenaeus, Origin, Tertullian, St. Cyprian, St. Athanasius, St. Basil, St. Augustine, Leo the Great, etc. etc.)
What you reference in the 13th century was the Fourth Lateran Council (1215), which did not invent the sacrament,
but rather instructed the faithful to confess at least annually. (You can read it here ->
http://www.papalencyclicals.net/councils/ecum12-2.htm#21)