"I'm going down to the River of Jordan / Just to bathe my wearisome soul" is a reference to Naaman in the Old Testament. In 2 Kings 5, the prophet Elisha tells Naaman to dip himself in the Jordan River seven times to be cured of his leprosy.
Although the focus is a bit different, the lines "If I can just touch the hem of His garment, good Lord / Then I'd know He'd take me home" seem to refer to healings that Jesus performed after the fringe of His garment was touched, first by a woman with a discharge of blood (Matthew 9:20-22, Mark 5:25-34, and Luke 8:43-48) and then by the sick people of Gennesaret (Matthew 14:34-36 and Mark 6:53-56).
The lines "I've got a home in that yonder city, good Lord / And it's not, not made by hand" are a reference to 2 Corinthians 5:1: "For we know that if the tent that is our earthly home is destroyed, we have a building from God, a house not made with hands, eternal in the heavens."
