I don't know about sinuses, but an MRI (WITH contrast) can rule out the possibility of an acoustic neuroma, a benign tumor of the inner ear (hearing nerve).
Acoustic neuromas usually cause gradual or (more rarely) sudden one-sided hearing loss and/or ringing in the ear, and can also cause vertigo or dizziness, although I think only about 5 or 3 percent of cases of unilateral hearing loss turn out to be acoustic neuroma, and dizziness/vertigo have many, many, MUCH more common causes than acoustic neuroma.
The MRI will likely not show anything--headaches and vertigo have many causes, most of which are not due to tumors or anything scary like that.
With headaches and vertigo, one possibility could be "migraine-associated vertigo." Check it out.
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