How would you diagnose this foot problem?

Sorry, I know this is a rather odd and, to some, disgusting question, but its been a bit of a concern of mine. Recently I've been having ungodly odors coming from my feet after taking off my shoes, and I'll shower and thoroughly clean them, only to have them smell again shortly thereafter. I recently completely washed my shoes and have been washing my feet multiple times per day, with no effects. I think it may be a result of having worn shoes for about 50 hours straight a couple of weeks ago, during which time I flew from Chicago to Minneapolis, before flying to Amsterdam, having a 10 hours layover where I toured the city (not removing my shoes, obviously), then flew straight from there to Tokyo. Does anyone know if this could be a cause, and, if so, what the solution could be? Other symptoms have included a bit of a burning feeling in my feet occasionally when I'm walking long distances and thus my feet are sweating a bit. Also, I've had a head cold recently, which, while I absolutely can't imagine would have anything to do with it, has coincided time-wise with the foot smell