No, you do not need to burn your socks if you get athletes foot. Athlete's foot is caused by a fungus, which lives best in warm, dark, moist places- such as found between your toes. There are multiple medications available at every pharmacy for treating it. Some of the preparations are creams, some powders, and some in spray or liquid form. In addition to treating your feet, it is often recommended that you treat your shoes, using the powder or spray, and then letting the shoes sit a day or so to ensure you have killed all sources of the fungus to prevent re-infection. Sanitize your socks by washing them in hot water and detergent, adding either bleach or an oxy-clean type additive. If you are talking about really fancy dress socks, a whirl through the microwave for a minute or so, while damp- will accomplish the same thing. Might not smell too good, but very effective. The best thing is to avoid getting it in the first place- protect your feet in places like public locker rooms by wearing shower shoes, the cheap ugly rubber things are just fine. After showering there, dry your feet very well and apply a medicated foot powder or spray. It isn't a perfect method, but it will help prevent most infections.
a career as a military medic taking care of too many guys with athlete's feet.