They could be an allergic reaction, flesh tone moles, warts or one of many other possibilities. I suggest you go to the doctor just in case it's anything serious but it more probably is nothing to worry about.
The white bumps on the feet can be seen as a depigmentation of patches of skin on the extremities, which is the most notable symptom of Vitiligo illness – autoimmune and inflammatory disease.
White bumps can be blisters appearing on your feet from shoes. Your shoes can either be to big or to small. When they are constantly rubbing your feet the friction can cause small blisters to appear on the sides of your feet as well as on the bottom of your feet.
They are called plantar warts and can be a pain. Go to your doctor to remove them and he will prescribe a medicine that can be applied for prevention purposes.