Could it be a level of racing thoughts or anxiety-provoked? Or some mild obsessive compulsive tendency? Or do you think the music thoughts serve as a less than healthy self medication, of sorts (like picking or teeth grinding habits)? Or are they possibly even non psychotic hallucinations? Getting to the bottom of that may be helpful in finding a way to stop them.

I wonder if in some way a medication could in some way be a contributing factor. But maybe not.

It's not freakishness. You are far far from being alone with this issue. I had a period of musical hallucinations, but they were likely a result of neurological issues. It sounds like you are saying yours aren't really hallucinations, though. Again, that isn't freakish. None of the causes I mentioned above, of music constantly in one's head, are that rare.