Could an internal clicking in my head be connected to a tumor?

Unlikely: Please see your md for a physical to be sure but such a complaint is rarely related to brain tumors.

Possibly: Tumors in certain parts of the brain/skull can definitely affect your hearing. Usually, however, this manifests as a hearing loss. Some disorders of blood vessels, such as abnormal connections between arteries and veins, commonly present as pulsatile tinnitus.