There can be a number of reasons for itching at the bottom of feet. It can be because of a certain kind of soap or shower gel that you use. You can cure it by applying anti itch creams like Hydrocortizone and/or Diphenhydramine. However, it might also be because of Diabeties, low back, periferal neuropathy etc and you need to consult a doctor and get tested for these diesease.
You may have some sort of fungus on your feet or you may be allergic to the shoes you are wearing. Or it could be the socks because you may be allergic to the soap or bleach if used when washing them.