Same, happening to me right now, happens automatically almost every morning when I wake up, which kind of gives me my own "soundtrack of the day" and enjoy the ride.
Sometimes the song is stuck in repeat though and the only way to kick it out of loop is to actually listen to it.
An interesting bit is that this internal jukebox is actually playing faster than real time, even though it sounds absolutely correct and natural in my mind and definitely not as if it was a 1.2~1.5x play rate that would give this funny "Benny Hill effect"; so when I perform the song at the time scale that I hear it it is clearly too fast (higher BPM) to outside observers or when compared to an original recording.
It's as if my experience of mind-time is skewed vs real time so I've developed a bunch of coping strategies like padding (e.g making every beat having a "late by ~x" feeling), forceful downclocking (some sort of detached zen mode where I let go of the internal clock, which gives a very surreal feeling of perceiving the world), or active continuous ratio compensating (sort of like the world is going at 0.8x compared to my reference clock so remapping makes it sort of bullet-timesque)
Socially it's all very disconnecting and exhausting.
In theory I could translate it to a DAW (but I'm not that great at transcribing music...it's possible, kinda, but slow), but I can't easily repeat the music in my head (not what I make up at least, proper released songs tend to be easier to repeat), so it would be difficult to recreate it enough to be worth the effort.
I wonder if it would help if I wrote a little program that plays short note sequences and then asks me to recreate the sequence (possibly modulo transposition).
Your ear (the ability to recognize intervals, scales, chords, chord progressions, rhythms etc) is one of (if not the) your biggest asset as a musician. And it's the only way to get the music out of your head, so cultivate it. Practice practice practice! Don't have to do more than a couple of minutes per day to see some results.
Ear training is something all creative musicians have to do. Many who are self-taught simply do it through picking up other people's tunes by ear (= transcribing), working it out on their instrument, starting with easy stuff and over time learning to "decipher" more difficult pieces. Dedicated ear training can really boost this process.