It's a pagan chant. I may have an author's name in a book; I'll look, but you might also try searching the singing group Libana, who perform it. The title is "The River is Flowing"' and you have all or most of the words above. Some folks sing "Father, carry me" as an alternating verse with " Mother, carry me", and some also sing "down" to the sea.
Those two, three, four line chants seem to get quickly separated from their author's names.
Blessings,
Barbara