Hi Tina, a kitty shaking his head doesn't mean he's got tinnitus. The only way you would know he's got ringing in the ears is if he tells you himself. With that said, kitty shaking his head could mean that there's an infection going on or maybe something is in the ear that you didn't notice.
You should take your kitty to the vet to get a correct diagnosis of his ear problem. I wouldn't just do some home remedy w/out knowing what is wrong....that could be dangerous.
Is this a confirmed diagnosis?
All I can tell you is with us humans, tinnitus is usually caused by a loss of hearing, esp high frequency loss.
Perhaps your kitty is going deaf?