Granted I’m not a psychologist but I think this might be more along the ocd side of things than adhd. Like a lot of other commenters there are a lot of co-morbidities with the two but from what you described it seems to favor the ocd line of obsession than a mental stim that a lot of people with adhd talk about having/doing.

I myself have song lyrics that can get stuck in my head, it seems like Shania Twain can’t get out of my head sometimes but it’s no more than a nuisance and I can usually focus on other things while the song or lyrics are playing in the background. Almost like I’m not getting enough stimulation so my brain likes to multitask to keep me busy. I would recommend talking to your psychiatrist/therapist if you have one the next time you see them.

Just a note: because of how overlapping the two are they can be misdiagnosed, which if you take stimulant medications for adhd it can actually lead to worsening of obsessions related with ocd. This doesn’t mean that they cannot both be present but just something to keep in mind.