Yes, the lipoic is very useful. Try it...

The fungus remains in the deeper tissues, when the skin heals up.

Biofreeze is not "cold"...it is at room temperature. What it does is the menthol in it stimulates the cold receptors in the skin, which then block the heat sensing ones, so the burning stops.In fact if your feet are red, the redness will remain. (redness implies increase blood flow there)

It does not make anything cold to the touch. It just "feels" cold.
Biofreeze has a non greasy gel base which is very nice. It sinks in quickly and does not stain or get messy.

Biofreeze also has a potent antioxidant in it, called Ilex. This is the same antioxidant in Yerba Mate tea, which is very popular in S. America. (more drunk there than coffee in fact).

The antioxidant is very useful IMO... as it takes down free radical damage from inflammation.