After three years of Paul’s conversion to Christianity—having an encounter with Jesus Christ, after His resurrection and ascension to heaven, see Acts 9:1-6, he visited Peter.
A Christian’s faith is not the source of healing. Jesus is the source. Jesus only responds when we exercise our faith in believing that He can do what we ask of Him if it’s according to His will (1 John 5:14).
The phrase “to reveal His Son in me” refers to Paul being used by the Holy Spirit, after conversion, to tell people about Jesus Christ and what He did for everyone on the cross.