If you can find a catchy song that you do like, you might be able to start intentionally playing that one back in your head to cut off the undesirable one. If it doesn’t work with the first song, try a song that has an unusual feature like a complex meter (5/4, 7/8, etc.).
You might be able to use that trait to your advantage by picking up an instrument if you don’t already play one. Sounds and music repeat in my head, and it definitely helped me with music. I also listen to music in the background whenever possible in order to drown out the other things. If you pick complex music to listen to instead of simple pop music, you can train your ears at the same time. I’ve been working on training my ears to detect microtones better lately, just by listening in the background.