The important thing about this is that the basic song is definitely in public domain. As long as you didn't do essentially a note for note recreation of another artists arrangement of a traditional tune, you don't owe anyone royalty payments.
There are lots of publishing companies(i.e.Hal Leonard) that would love you to believe that they hold copyright to any iteration of a traditional song because a version has been printed by them. Sorry, but Hal Leonard doesn't own the rights to Barbara Allen.