Baptism does not remove your sins. Only the blood of Christ. We're getting into the multiple steps of regeneration. My belief is that you're saved the moment God wishes to give you a new heart. The rest are the results of God's work.
" My belief is that you're saved the moment God wishes to give you a new heart."
That may be your belief, but it is not what the Bible clearly states. Yes, the blood of Christ removes sins, but the key is this: At what point do we come in contact with the Blood?
According to the Word of God, baptism is for the remission of sins (Acts 2:38) and washes away sins (Acts 22:16). In Matthew 26:28, Christ uses the exact same language that is used in Acts 2:38 to say that He shed His blood for the remission of sins. There is an obvious connection here. By submitting ourselves to His will and being baptized, the precious blood of Christ is applied.
I believe the hardest part for you in regards to baptism is that you think it negates God's grace somehow to believe that baptism is necessary to accept God's gift of salvation. Nothing could be farther from the truth.
God was under no obligation to offer us a way to be saved, but He has done so because of His unconditional love for us. That is what makes the gift free. We did not warrant the gift, but it was given anyway. The fact that we must obey Him to accept this wonderful gift in no way changes that.
God has always commanded obedience from His followers, including the Nation of Israel under the Mosaic Law. Please consider the following verses:
Hebrews 5:8-9 -
8 though He was a Son, [yet] He learned obedience by the things which He suffered.
9 And having been perfected, He became the author of eternal salvation to all who obey Him
As you can see, Christ is the author of our salvation, but only to those who obey Him. The only way to obey Him is to keep his commandments (Luke 6:46).
God bless.