This isn't the worst thing that could happen to you. I work with autistic pre-schoolers and I have found myself singing songs about brushing my teeth. I'd much rather have your problem.
Oh man, I feel your pain.... Songs can get stuck and just never come out! I teach pre-schoolers gymnastics and some of those songs stick like glue to the memory!
My mom runs a daycare at our house and for the past 10 years we've had kid songs and songs from kid's TV shows in our head. You know it's bad when you start harmonizing to the TV theme music as soon as it comes on.