Sounds like you might have used a solution of potassium permanganate that was too strong. The solution should be a very light pink. Too strong and it removes the fats from the skin and causes the symptoms you describe. Naphtha, like from an overfilled Zippo, has a similar effect. The skin dries, cracks, peels and leaves a red and raw area that takes a long time to heal. Potassium permanganate is strong stuff so if you use it lean toward a weaker solution.

It shouldn't redden or excessively dry the skin. Potassium permanganate is more appropriate for a fairly serious fungal infection not routine maintenance. But the solution just performs a knockdown function. You need to follow with extra care keeping the area clean and dry while the normal flora reestablish. I have found that zinc oxide is a good follow up and general preventative. In the field, particularly when I can't wash, I smear on a light coat of zinc oxide on the groin and between the fourth and little toes once or twice a day as a preventative. Don't let the potassium permanganate crystals contact the zinc oxide, or any other compounds.

In my experience the key to avoiding a flare up of athlete's foot or crotch corrosion is to avoid contact with soap. Wash those areas with water alone. Enough soapy water will wash down on groin and feet during a shower to take the human grease off. And after all else, before stepping out, rinse off again to remove every trace of soap.