Kitt is correct in that known reversal treatments for CMT are not known yet (other than some weak studies on one variant of CMT using Vit C)

However, it is rare for a neurologist to recommend supplements these days, IMO.

Alpha lipoic has been improved to r-lipoic which allows for lower doses.

The most common side effect for alpha or r-lipoic is stomach upset. But only 2 people here over the years have reported that.

Both are rather benign to take. I would start seeing effects in a month or so. Maybe longer. After six months with no effect, I think you can scrap them.

Alpha lipoic depending on doses may lower blood sugar readings. So diabetics should test blood sugar while using it.

Both supplements have long histories on PubMed around the world for being helpful for PN. (tested on diabetics).
HIV patients taking drugs for that use acetyl carnitine to minimize the PN that comes from those treatments. Also chemo.

Both supplements enhance mitochondrial functions of the cells. Your response to them, will tell your neurologist what your probable cause is, I would think.