I see it a little differently than you are articulating.
Here's the picture: We go to the Jordan river and hear John preach to turn to God because the kingdom of God is at hand ie: the Messiah is coming. I'm convicted and decide to be baptized by John. He has those of us going through the conversion process...get in the water and publically confess our sins ...then he dunks us (not sure if he baptizes in his own name or not).
After we believe, repent, confess, and are baptized, John preaches that he expects us to produce fruit/actions/works that witness to the fact that we really have repented of our sins/turned from our sinful ways.
Mark 1:4 John did baptize in the wilderness, and preach the baptism of repentance for the remission of sins.
5 And there went out unto him all the land of Judaea, and they of Jerusalem, and were all baptized of him in the river of Jordan, confessing their sins.
Matthew 3:5 Then went out to him Jerusalem, and all Judaea, and all the region round about Jordan, 6 And
were baptized of him in Jordan, confessing their sins. 7 But when he saw many of the Pharisees and Sadducees come to his baptism, he said unto them, O generation of vipers, who hath warned you to flee from the wrath to come? 8 Bring forth therefore fruits meet for repentance: 9 And think not to say within yourselves, We have Abraham to our father: for I say unto you, that God is able of these stones to raise up children unto Abraham. 10 And now also the axe is laid unto the root of the trees: therefore every tree which bringeth not forth good fruit is hewn down, and cast into the fire.
11 I indeed baptize you with water unto repentance:
John baptized them unto repentance...works do not come before repentance yet John baptized unto repentance not after repentance and works. It's a BAPTISM OF REPENTANCE for/in order to remit sins.