This very similar to my situation with ENT and PT. Cardiologist referred me to neurologist to role out peripheral neuropathy. In fact I was diagnosed with motor-sensory poly peripheral neuropathy. I’m not sure I understand the dizziness and unsteadiness mechanism but I think maybe because proprioception. An early PT worked on balance, but more so on strength, her rationale being (I think) if I could improve my legs and core strength, I will be more likely to catch myself and reduce my falling if/during my dizzy periods. I’m a 69 yo dentist and travel internationally on a monthly basis in medical teams treating refugees and indigent. I have described walking as if I were wearing ice skates.