Welcome, Hot feet!

Neurological problems are very weird, and answers aren't easy to come by. Shoes that are irritating your feet in some way might indeed be the problem, as Jomar suggested. Maybe even the socks you wear? There's a big difference in socks--what they're made of, their thickness, etc.

You don't mention how long you've been taking the iron supplements but you don't get an immediate effect from them. It's a slow gradual improvement.

Cold hands and feet can be a symptom of iron-deficiency as I understand it.

You might want to try experimenting with more exercise, less exercise, or different types of exercise, especially if the exercise involves the legs and feet.

I'm sorry I can't say anything more helpful. I hope things will get better for you soon.