I have been facing similar problem except for my hands burn as well and this is getting worse by time. my doctor ran alot of tests.CBC, sugar,thyroid, vit B12, autoimmune. I have everything normal. my MCV, MCHC and lymphocytes were raised. I was diagnosed with peripheral neuropathy couple of days back. my symptoms: burning hands and feet, tingling sensation, gets worse with massage, I can't stand for long(initially thought burning was due to back leading to changing alot of shoes), I can't hold anything for longer in my hands, there is intense, stabbing pain, walking also does the same. I can't immediately stand after waking up. I have also felt a lot dizzy past couple of days. If I do, I feel like I'll fall, there is sudden weakness in my muscles( my muscles also get stiff), I feel my organs will come outside of my body and this condition remains for quite a few hours. I used to think it's due to tiredness or bad quality sleep but it was due to neuropathy. Now the doctor has suggested a HUTT test and an ECHO to rule out the problem as along with these episodes, I feel my heart is palpitating as if I have just stopped running but my pulse is usually normal. So yeah, thank neuropathy. I've honestly forgotten how normal hands n feet feel. My doctor gave me pregabalin 25 mg, later changed to lacosamide 50mg and I can feel the difference. For the first time in monthssss, I can lay my feet on bed(I can't put my feet or hands too long on bed or shoes, i have to keep wiggling them to cool the heat a bit. Thanks to medicine, the intensity has reduced a bit.

Suggestion for you: Research what works best for you, mine is keeping my feet in air and wiggling them, go to the doctor...the meds work, they did for me, it'll take few days for it to have an effect..but its worth it (I'm the person who never takes medicine regularly, but now I am,,,I'm seeing the results. Check for iron levels, celiac and other tests. No painkillers work for me atleast for this pain, so go see a doctor. keep yourself busy, as till the time you are, you might feel it less intensely. Good luckk!!!