My diagnosis is idiopathic small fiber peripheral neuropathy, which is generally a purely sensory problem. However, nothing regarding PN is simple, and I believe it is possible to also have autonomic symptoms with this diagnosis, especially as the disease progresses.
I too have dizziness, but I believe it is probably due to orthostatic hypotension, which means one's blood pressure drops when standing up. I have high blood pressure (HBP), for which I am taking 2 medications. My blood pressure is a little difficult to control (which may be due to PN, or not), so sometimes it is a bit too low, which results in the orthostatic hypotension noted above. When dizzy upon standing, I have measured my blood pressure, and found it low.
If you also have PN and HBP with occasional dizziness when standing, I suggest you discuss this with your PCP. It may be possible to help this problem with an adjustment of your HBP meds.
As an aside, there is a difference between dizziness (feeling faint) and vertigo (a sense that your surroundings are spinning around you). This should also be discussed with your PCP to start. No need to see a specialist unless referred.
Hope this helps.