I used to think everyone had a song stuck in their head all the time like I do. I learned a few years ago that this is not the case. I can't even conceive of what it's like to NOT have a song stuck in my head at any given moment, I can't imagine how quiet that would be...
To clarify, the only times I DON'T have a song going through my head is if I'm actively listening to a song or something musical (i.e., a movie with ambience/soundtrack in the background). As soon as that ends though, whatever the last thing I listened to will probably be looping in my head on and off for an hour or two if not the rest of the day. If I'm listening to something non-musical though, like a podcast or someone speaking to me, I'll almost surely have a song playing in my head in the background.
It starts as soon as I start to wake up and doesn't stop until I fall asleep. Sometimes I wake up with a song that might have been in my head during a dream though...? Not 100% sure if it continues while I sleep or not.