If the ambient temperature is hotter than your skin temperature, it won't provide cooling with more wind.
You can get some more evaporation with the wind providing a cooling effect while you sweat, but it is different than the wind chill providing convection transfer of heat.
But the cooling effect from evaporation is considerable. Do you live in the South? When the air is still and the humidity is very high here, your perspiration just sits there on your skin and you get hotter and hotter. When there is a breeze the evaporative effect is significant for cooling.