According to this link, the "burning" sensation on soles of feet is actually caused by low B5 - often revealed/starts after beginning supplementing for low vitamin D
I have had this burning feet and very sore heels too. (Plantar fasciitis) This all began about a month after starting vitamin D supplements (quite high dose - 6000iu daily) This high dose is only very slowly increasing the vit D result.
I added good quality Vitamin B complex last week (Thorne's) - within 48 hours the burning had started to fade.
More interesting, after a week on B complex, pins & needles all over started, assuming this is low B12, (revealed by supplementing B complex?) Just added b12 oral mouth spray by Better You.
All my recent BH blood tests during last 18months showed very high (often above range) B12 and right at top of range, folate UNTIL I started to correct my low vitamin D. Fallen slightly in last test.
My vitamin D never appeared very low (lowest was 33) BUT I have just finally been diagnosed with significant gluten intolerance/ possible coeliac. I think, with gluten intolerance, the vitamin D level can, in reality, be significantly below the test figure (due to low nutrients across the board)