Maybe google Raynauds'? The discoloration in three stages, the relation to cold and the shooting pains sound more like vasospasm symptoms than neuropathy.... When all you have is a hammer, every problem is a nail; I think your GP isn't looking beyond the diabetes. Just something to research, maybe. The condition runs in my husband's family. My father-in-law fell in love with "the girl with the cold hands" at a dance where they had to switch partners all the time, and their grandchild (our nephew) was born with purple, ice-cold hands, making a lot of alarmbells go off in the NICU. My husband does have it, but not as bad as his sister does. It mainly affects the extremities in cold weather, and there are special gloves and socks that can help. Plus, you know, heating pads and keeping warm, trying not to stress overmuch, no smoking etc... Theirs is primary Raynauds, but secondary is more likely if it came on late, and if it hasn't been with you for life.
Not diagnosing, mind you... Just an avenue to explore, as you're not convinced it's neuropathy, and the meds aren't working.
Good luck!
Jo
PS: Link for thoroughness->
https://www.hopkinsmedicine.org/health/conditions-and-diseases/raynauds-phenomenon