This is why we should baptize in the name of Jesus. In every thing Jesus should get the glory. Was it repentance, baptism, in the name of Jesus, two of them or all three of them that produce the remission of sins. So many scriptures state that believing in Jesus produces remission. It's the calling upon Jesus that cleans sin.
Baptism is a symbol for cleaning.
Paul was baptized after his healing and being filled with the Holy Ghost. I thing he was forgiven of his sins before his baptism. The baptism confirmed who was his Lord. It's the resurrection of Jesus that saves not the water which can only wash the filth off the flesh. This is just like the above scripture showing a washing in the inner man.