Raw feet? Epsom salts shouldn't cause that, but they will sting, if used on raw skin.

I wonder... do your feet normally sweat when you wear socks?
If you normally sweat and there is a residue in the socks of soap and/or fabric softener, this will dissolve in the sweat and burn and irritate the skin on your feet.

If so, I am going to suggest that you give your clothes an extra rinse when washing them. Lots of soap will come out during that second rinse...if you watch it you'll see. Then DO NOT use a fabric softener. The chemicals in fabric softeners can cause all sorts of skin grief.

Also if you have athlete's foot, you will have red/raw skin on the bottoms of the feet. Sometimes people think their fungus is gone, but it is still living in the deeper areas of the dermis, and can cause burning by stimulating the nerve endings there. If you had athlete's foot in the past, I'd suggest using Lamisil for a week and see if things improve. Lamisil is the strongest one out there and there is less resistance by the fungus to it.