An EEG/NCS (nerve conduction study, usually done along with the EEG), can differentiate between large and small fiber peripheral neuropathy. With the usual symptoms, that is often enough to make the diagnosis of small fiber PN. Many patients do not get the biopsy for that reason, so your neurologist is probably correct.
I have small fiber PN, and I had the nerve biopsy because I insisted on it, because I wanted to know "for sure". It was positive, but has made no difference in my treatment, so it was unnecessary from a medical point of view.
BTW, the test is very expensive, and only available from a few labs. It may be that your insurance will not pay for it.
As everybody on this forum knows, this is a weird and frustrating disease. Hang in there, and don't get angry. It won't help.