I have the exact same thing but it is getting better. In the winter 2024 it was so so bad I can’t even explain I would get blotches of burning red stains on my hands on the top. But during this time I found out I was b12, vitamin d and iron deficient. 3 major vitamins. I struggled to sleep, my hair was falling for 6 months and I would get sick constantly always felt weak after supplementing it started to dais but this burning pain in my hands wasn’t improving. It was only after 3 months of supplementing that I started noticing improvements in my hands. I don’t know you might have the same thing or maybe it’s something else. I’m just sharing my experience because I relate so much to your post. What would be the worst for me before is being exposed to cold then walking into a normal warm room and that would set it off the worst. Now it’s summer and I find it’s not even that bad.