Hi and welcome, your spine does sound very suspicious but it still might not be the cause, i think its very well worth looking into though, if you can get an MRI on your whole spine as it may show if there is any pressure causing this to affect your feet, normally pressure on your lower spine affect your feet but it can come from the cervical spine as well.

As far as soon as you take your shoes off you feel better, well anyone with small fibre damage in the feet, normally can't stand wearing normal type leather shoes, usually aggravates the heck out of them, as there are many,many small fibre's at the surface of the skin, the small fibre's job is send correct signals concerning heat, cold and vibration to the brain, when there damaged they send confused signals that's why you feel that burning feeling and its very common for the feet to burn more at night, some can't even stand bed sheets on them, which makes me ask, are your feet sensitive to touch? or have you any numb spots any were on your feet ?

Loosing patches of hair, have you been to a dermatologist ? Alopecia comes to mind, someone correct me if i am wrong but i think i can be caused by the immune system, autoimune problems can be asociated PN, like Hypothyroidism and another is Celiac disease which one symptom is diarrhea.

I would defiantly take notice of the previous posters and i would get a refferal to see a neuro that is a PN expert not just a normal neuro, to get all appropriate blood and other tests done.

good luck
Brian