Is it possible to ever reach a point that I don't sin?
There is no way that your life can be completely free of sin on this side of Heaven. All believers will be completely sin-free upon entering Heaven, but this won't be because of what we do or don't do. It will be because of what God does in us. "Nothing impure will ever enter it, nor will anyone who does what is shameful or deceitful" (Rev. 21:27).
God calls us to rid our lives of sin. We are to live in a way that is pleasing to Him, casting off as much of the world as we possibly can. "Let us throw off everything that hinders and the sin that so easily entangles" (Heb. 12:1). If we could possibly be completely sin-free, then Jesus would not have had to come and give His life as the penalty for our sin. But He did, in fact, need to be the perfect sacrifice for our sins so that we, through Him, could have eternal life.
If your desire is to please the Lord and to live for Him, then He will guide your steps away from sin through convictions brought into your heart by the Holy Spirit. Speaking about the Holy Spirit, in John 16:8, Jesus said, "When he comes, he will convict the world of guilt in regard to sin and righteousness and judgment." Just seek the guidance of the Lord and pray for Him to give you the strength to cast off your worldly desires and the sin that so easily entangles you.