Hello! Particularly if the pulsing sound is just in one ear, a CT scan without contrast can still be helpful. The bone structure around the inner ear and the nearby blood vessels can be evaluated without contrast, and sometimes this gives useful information. MRI scans are also useful in many cases, and the contrast agents are different - it would be unusual for somebody to be allergic to MRI contrast (gadolinium), and an allergy to CT contrast (iodinated) is not a contraindication to giving gadolinium.