This is probably due to athletes feet fungus. This is caused by the condition of the shoes being to wet and allowing the fungus to grow on your feet this causes irritation.
This could very well be a heat rash that is occuring at the bottom of your feet. Keep your socks dry and ensure it is not athlete's foot by using powder.
This could be athlete's foot. If you are a diabetic you should always check for foot rashes. Red rashes that are not itchy soles of feet can be syphilis.