It's really itchy between your toes, it kind of stings and the skin's really tender, there's a good chance you've got athlete's foot or foot fungus.
And yes, you can get it even if the only warm and damp. This can happen if you don't change your socks regularly, or if you don't dry between your toes after having a shower.
If you've got athlete's foot - don't keep scratching where clear up after a few days, but keep putting on the cream for a couple of weeks after. You can get these creams at any drug store, without a prescription.
So if you don't want itchy feet and don't want to make people puke everytime you take off your shoes, make sure you change your socks every day - maybe twice a day, if you your shoes - it's probably time to do something!