What you are describing is commonly referred to as "Musical Ear Syndrome."
The first time it happened to me, I was worried it was an hallucination until I researched the phenomenon a bit more.

It is commonly seen in people with lack of sleep, tinnitus, and hearing impairment or hearing loss. It can also happen more frequently when your environment is particularly quiet.

There is a growing collection of literature online about this, but the take home message is that this is a common phenomenon even in people without any history of mental illness.