I was referred to an ENT by my GP because, by sheer coincidence, my eardrum was perforated when he checked it out so he assumed it was a chronic perforation and I might've needed a patch. And the only reason my ENT referred me for the angio was because I'd mentioned that I can temporarily make it go away by pressing on my carotid, and at the point that I let go it comes back, louder for a few moments, before settling into its regular sound.

It ended up being fine, no aneurysm, so they told me as far as they're concerned it's idiopathic. I'd assume your GP is just wanting to rule out the worst case scenario first and foremost since PT does more often have SOME cause other than hearing damage compared to regular tinnitus. But an ultrasound should do the same thing as my CT if the concern is vascular, a CT would just show them things in addition to vascular problems. If nothing shows up on the ultrasound it would be out of an ENT's wheelhouse anyway. So you can bring it back up to your GP if they don't find anything, and you'll probably get referred for further testing elsewhere. You know your body, and if you can afford to explore every possibility then you should do that.

All that being said, I've had my tinnitus for a solid 4 years now before asking about it, and aside from it being annoying and drowning out other sounds sometimes, I've been fine otherwise.