The only time you need additional testing is if you have symptoms that might indicate vascular compression of either the internal carotid artery or internal jugular vein. I was diagnosed only by a CT w/o contrast prior to having my ES surgeries. That was all that was needed & both of my surgeries turned out to be very successful.
Here’s a post @Jules wrote that give information about vascular symptoms. In the absence of these, the scan you’ve had is enough for a doctor to diagnose you & offer surgery.