Jesus not only became a curse, that the power of the curse over us might be broken; He also became sin, that the power of sin over us might be broken.
Jesus created the new covenant, a covenant based on the shedding of His blood at the Cross. We see this in the Lord's Supper Mark 14:22-24.
Hebrews declares that the new testament in Jesus' blood is even better that the sacrifices of animals blood in the old testament Hebrews 8:6. He is also mediator of the better covenant, which was established on better promises.
When we receive the Lord Jesus, we enter into a new covenant and a new righteousness; His righteousness. He accomplished it all for us, forgiveness of sins and healing for our bodies. This new covenant is no less a healing covenant than the old covenant. It is even better because Jesus Himself his the healer and is now in us by His Spirit.