My chiro explained part of it to me in this simple way,
nerves talk to and control the muscles and relay sensations.
the nerve/muscle connection really fits for me with the achy muscle stuff I get in my neck, upper back & armpits {pec minor}

The first cold front & frost coming in this weekend and my neck has been sore & achy since yesterday- for no reason other than the weather changing.
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I'm thinking if you don't have swelling or color changes {more vascular in nature} and just have the coldness sensations then it seems like it would be more nerve related.
But it is very confusing when you have the smaller sensory nerves as well as the large nerves involved.

I suppose the drs are meaning the main nerves ulnar, radial, median when they label it as neurological. Just my thoughts on that.

I only had some ulnar nerve involvement for a couple months, yrs ago.
Luckily had a good enough PT at the time that it was able to be resolved.
Plus I was doing Sharon Butlers stretches, extra vitamins & supplements, heat/ice and I was off work by then, so lots of R & R.

But if I lift heavy things too much I'll get an achy feeling in my elbows and in my wrist.

I think I am mostly myofascial sx now, but still lose arterial pulse when arms are up/out or in other extreme positions..
I can hold them up or out for a minute or 2 but I can tell the blood stops and they get heavy and sore.