I was diagnosed with small fiber neuropathy.
My neurologist said either my celiac disease or the CVID can cause neuropathy. She wasn't sure which had caused it. (If you have CVID and the gene for celiac disease you are likely to have both, so I figure I was doomed either way.) My neurologist wanted me to start on IVIG (I was not so low that they could put me on IVIG for CVID yet). They have to put you on a higher dose for neuropathy than you are put on for CVID. Anyway, I decided to see if my symptoms would respond to a gluten-free diet and they did. I was entirely in remission until I was vaccinated for COVID when they flared back up in a monstrous way (I keep winning the jackpot). They are thankfully, flared back down somewhat but no booster for me.
Anyway, CVID does cause neuropathy for some, but not all. That is what the V stands for, "variable".
You may want to be tested for celiac disease while you are at it. Oddly, most doctors do not think to test for this. About 30% of us carry the gene for celiac disease and where you have CVID (which is likely to trigger it), it is worth ruling out, in my opinion.
If you do have neuropathy and celiac disease you are much more sensitive to gluten. They thought, at one point, that I had refractory celiac disease because I was not improved on a gluten-free diet. One of my doctors guessed that the gluten free pizza I was eating was likely cross-contaminated and just like that my symptoms vanished. I can have gluten free pizza but it has to be "certified gluten free".
Anyway, good luck to you. I know this is overwhelming.