Both of these benefits are mentioned together as part of the salvation package (Psalm 103:2-3, Isaiah 53:4-5, 1 Peter 2:24).
It should be noted that healing in the New Testament is not referring to healing of the spirit. The spirit cannot be healed, but can be regenerated, or "born again", or "born from above" (John 3:3-6, 2 Corinthians 5:17).
Jesus has done His part. He sat down at the right hand of the Father. It is now up to us to receive what He has provided according to Romans 10:9-10. Believing with the heart and confessing what God has provided is essential to receiving anything that God has already made available to us.
Mark 11:23 says "Whoever shall say unto this mountain (sickness or spirit of infirmity) be thou cast into the sea and shall not doubt in his heart, but shall believe that those things which he saith shall come to pass, he shall have whatsoever he saith". We just need to know what Jesus purchased for us when He was beaten, hung on the cross, sentenced to hell, and then rose victorious over death, hell and the grave.
He has given us authority (power) that He purchased for us (Matthew 28:18) in order for us to go and do the work that He began when He walked the earth as a man (John 14:12). You have been provided your healing by Jesus.