If God punishes sin and I will always be a sinner, being a Christian or not, I will always be punished.
I think your question misunderstands God. First, believers who except salvation through Jesus Christ are not sinners. They were sinners, but now they are saints. Being a sinner and sinning are not the same thing. Being a sinner refers to the fallen nature of man. Sin is an action under the law. In the regeneration we have a new nature, which is Christ's. Adam and Eve were created perfect, yet they sinned. They became sinners when they sinned and their perfect nature was changed into a sinner's nature. That does not happen to believers. We may sin by an action, but our nature does not change. Adam's perfect nature was not the divine nature. Believers in Jesus become partakers of the divine nature which can not change. This nature is in our spirits which have been born again. However, our souls and bodies have not yet changed. We can modify our souls by renewing our minds, and we can use our bodies as vessels of righteousness, but choosing to sin does not change the divine nature that has transformed our spirits which have been sealed by His Spirit.
Furthermore, your question begins in the law, not grace. We have been reconciled to God through Christ and are not under the law. Indeed, gentiles were never under the law. The law was given by God only to Israel to magnify sin to show the folly of self righteousness and to show the need for a Saviour. Until Moses there was no law, nevertheless death reigned. That means that sin exists, but God did not impute sin until the Mosaic law. Under Christ the penalty of death has been paid. God does not impute sin to the believer even though sin may exist.
Second, God is not punishing sin. Sin is its own punishment. Chastisement of believers is correction, not punishment. God came to restore life, not destroy life. It is a mistake to look upon Old Testament saints and make them equal to New Testament believers. They are not equal. Jesus said that John the Baptist (an Old Testament saint, as was Jesus) was the greatest of all OT prophets, nonetheless the least in the Kingdom of God (NT saints) is greater than John. Why? Because the OT saints did not have the permanent regeneration of the resurrection. John had the Holy Spirit from birth, but could not participate in the resurrection of Christ since he died before the resurrection. Likewise, Heb 11 states that the OT saints died waiting for the promise of the better thing provided for us. God does not change, but he does change the way he deals with people.