I feel you bro. I can't tell you what it is, but I can tell you about my peripheral neuropathy (PN).
I had myself convinced I had neurological disease too. I couldn't understand why it came on days after quitting drinking. There are 2 reasons the dr gave me. First he told me that my neurochemistry is rebalancing, and it's literally a stress on your nervous system while this brain chemistry clears up. Second, he talked about how alcoholics bodies, at a cellular level, actually function better for short periods with alcohol. At the same time alcohol is killing you, it provides a very short-term bridge over gaps in your nerve communications system (that alcohol created in the first place, mind you). In sudden sobriety, these gaps are suddenly apparent. There's no "lunricating" affect of alcohol. These gaps cause things that are weird involving electrical impulses that are nerve signal transmission.
For me, it was the pins and needles, cramping, spasms/twitching. It was worst in my hands, but I could and did twitch everywhere. For months. Other weird sensations (parasthesias in medical speak) involved a feeling of weakness in my grip (without actually being noticeably weaker), "buzzing" or shocking (felt like electrical fleas), feeling like I had water spots on my legs (but didn't), a lower left eyelid that twitched for weeks, like a twitch a second in my calves for long periods after exercise, restless leg syndrome, myclonic jerks (I.e. Flailing body parts while drifting off to sleep). Fun stuff.
So neurologists are really good at nerve stuff. I had to see 3 before I got all the answers tho. Withdrawal also messes with your brain, giving you evil recurring thoughts. So see who you have to see. But I still have some issues after 10 months. They have gotten better. My neuro thinks I will make a full to partially full recovery which is fine - I am fortunate that my symptoms are a distraction, not painful or debilitating.
The other thing he told me to keep in mind, is that medical folks don't have this all nailed down. PN is permanent in some people, while others recover quickly. there are a lot of unknowns on how nutrition, time, and cumulative impact make healing easier or harder. Symptoms can come and go for a long time. Good luck,