No, you're ABSOLUTELY not the only person who has music always stuck in their head. And I think Alex is right about the whole thing. If you have something like that, where it can play in perfect accuracy and tone in your head, and you can remember every detail - just take it as a gift.
Myself, sometimes I can hear Mozart, or even Evanescence clear as day in my head. I even have a friend who has a telekinetic gift to be able to tune into radiowaves sometimes!
-youngprer