Their is original sin and their is sin. We cure original sin by faith in Christ and are born again. Until then we can do nothing about our sin. After we are born again, Christ in us removes our daily trespasses.
When we are truly “Born Again” the Light of God that shines through us as the Holy Spirit (Thus the phrase “Born of the Spirit”) radiates out of us and protects us from sin.
This is how Jesus healed by forgiving sins. It was the Spirit of His Father in the form of the Holy Spirit working through Him that removed the sins from people’s souls.
A spring flowing clean water outward will never allow dirty water to flow inward. This is why Jesus could be with the thieves and tax collectors and not be harmed by their sins..