What the OP is experiencing is called "sound or auditory hallucinations" or "musical ear syndrome". I have had it for years, and it drives me crazy. I have a song or music without words playing in my mind every waking minute of my life since about 5 years ago, and I'm 76 now. The song may change several times a day, or my mind may simply make up a song that I have never heard before. Some of the songs I recognize and can place the singer(s) and even the circumstances in my life where and when that song played an important part. Other times, I recognize the song but just can't place it.
The music never goes away, but I have learned by experimentation that if I go to YouTube and find a song or songs that I really like, for example, a contemporary Christian song, then that song will be cast into my mind and replace some of the unwanted songs that fill my head. I have also discovered that if I start to count to 50 in my mind, that distraction will cause my mind to stop playing the song, and even forget it, and replace it with another as if I had just changed the channel.
I recently visited a mental health physician, and he recommended that I try a medicine called Risperidone. He insists that some of his patients had good results from that medication. I used it for one night and had terrible side effects, so I immediately gave up on it. It is also highly addictive, so I suppose I will simply have to learn to live the rest of my life with this affliction. You can check it out here:
https://en.wikipedia.org/wiki/Auditory_hallucination