That sounds like something I've had for about a year or 2. I started hearing a sort of short buzzing sound off and on and realized it coincided with moving my head or turning or even looking from side to side, and it was accompanied by a brief feeling of dizziness.
My dr sent me to a dizziness and hearing clinic for testing, which was weird. They put a big helmet on my head with a camera focused on one eye. They had me read and then watch things move on a computer screen. Then they had my lie on a table with my head over the edge resting in the tester's hands. She moved my head around. She also had me look to one side at a 45 degree angle and sit up.
All of this was to see if I had Nystagmus, which they didn't mention at the time. Picture a cartoon character with their eyeballs twirling around. It's actually just a slight vibrating rotation. A few days later they called to set up an appointment to have my "crystals rearranged". I was like "What?"
It turns out that there are crystals in a little sack in our ears. Who knew? Sometimes some can migrate out and get into the semicircular canals and cause dizziness and sometimes sound effects. The Nystagmus is a marker for it. The treatment is just manipulating the head position around in different ways to try to get them out of the canals. They also gave me some anti dizziness exercises to do.