Welcome @corne, You are not alone with the burning of the feet. I just have the numbness but there are other members who share your symptoms. Here are a few discussions you might find helpful.

-- Erythromelalgia: https://connect.mayoclinic.org/discussion/erythromelalgia/
-- Peripheral Neuropathy vs. Erythromelalgia: https://connect.mayoclinic.org/discussion/peripheral-neuropathy-vs-erythromelalgia/
-- Erythromelalgia and Myeloproliferative disorders: https://connect.mayoclinic.org/discussion/erythromelalgia-and-myeloproliferative-disorders/

Have you been diagnosed with peripheral neuropathy?