My hands and feet are always burning up. Even in the winter. It is so hot that I can't even sleep. What can cause this?

Acrodynia. The best sense i can make out of the symptoms you report is a rare condition called "acrodynia" (which means painful hands & feet). This is usually due to heavy metal poisoning like from mercury, etc. Otherwise you may have a painful peripheral neuropathy, which can be due to something like a cyst in the spinal cord or from unknown causes. Best to see a doctor to clarify.
Neuropathy. Can cause burning. You need to be evaluated by your family dr.