Have an Answer?
My immediate thought was: Theater.
Theater combines all three. Where I attended college, their Theater program had a "Storytelling" course, where you write and perform stories, learning techniques to different types of storytelling. It sounded really cool, but I'm simply a writer, so I never explored the speaking, acting and singing realm of storytelling.
Whether you pursue it as a professional degree or a career, I think Theater is a great option.
I was going to say Public Relations, but I don't think there's much acting or singing there. Maybe something in Film/Video, too, could be an option.