Better yet, Poe had a Raven rapping at his door, you've a sparrow. Somehow also become immortal from an avian visitor?
Poetry, the obvious solution.
Exactly. Just allow the bird to keep pecking. Whilst it will gradually drive you in to the depths of utter madness, everyone knows that insane people create the best art (see: Poe, van Gogh). You may be too insane to care, but someday, after you die and somebody digs up your poetry journal from your house which is bizarrely decorated in swathes of sparrow-worshiping paraphernalia, you will become immortal.
Sparrow, sparrow, ever-pecking
Pecking at my window-sill.
Do you desire seeds and water?
What need can my window fulfill?
Or do you want to enter, flying,
Flying into my demesne?
What is it you'll gain by pecking
Always pecking at my brain?
Pecking, pecking, ever-pecking,
What is this most dour refrain?
What is it you want from here,
Why do you still peck and leer?
Why do I continually hear,
Rapping, Tapping, PECKING STILL!