I also suffer from burning feet, the pain gets unbeable at night time and as Sheltiemom said Alkaseltzer helps me to get enough relief to fall asleep.
I also try lukewarm Epsom salts footbaths, I need to steep for at least 30mins and the relief can carry on to the next day.
I am trying to replace the footbaths with Magnesium oil, only due to my skin becoming like leather with the footbaths
The other relief I get is from Lignacaine Infusions from my Pain Management team, this gives me around 3 weeks relief at a time. I go into hospital for a 90min infusion and experience 3 days of increased pain and then the pain settles for 3 weeks and slowly comes back, i only have the infusion every 6-8 weeks.
Good luck