It is possible that you are suffering from peripheral neuropathy. This is a condition that affects the nerves in your body outside of your central nervous system. It often starts in the longest nerves of your body, which reach to your toes and your feet. There are many possible causes and it often improves with treatment of the cause.
the most common cause for this is athletes foot. Usally it can be treated with a over the counter spray or cream. If you have a more severe case you may need to see your doctor for a perscription cream.
There are two conditions that could cause this sensation. First of all your feet could be very sensitive to changes in blood pressure, when you lie down the venous pressure drops and that could cause your symtoms. More likely you have a fungal infection of the feet "Athelete's Foot" see a doctor for an anti-fungal medication.
This could be occurring because your capillaries are bursting or because of some form of psychosomatic disorder. I would recommend consulting your physician.
It could be the circulation in your legs. If you have been on your feet a lot during the day, they could burn from that. Also, if there is a problem with being overweight, the amount of pressure on your feet can cause it.
This is something you should talk with your doctor about it could be anything from Athletes feet to diabetic Neuropathy not knowing your medical history hard to say.