The body may sweat during swimming, with the moisture dissipating unnoticed in the water.
You do not necessarily sweat when you swim, but if you swim long enough and hard enough so that the exercise raises the internal body temperature, then you will sweat.
This can be proven by measuring body weights before and after exercise.
As to the question of discomfort when temperatures are in the nineties, the body’s metabolism is continually producing heat, some of which is ordinarily lost to cooler surrounding air.
But when the ambient temperature equals the body’s core temperature, it is well above the skin temperature, so the body is gaining heat from the environment, instead of radiating it, as would normally happen.
So at high temperatures, the heat builds up and we feel hot.
Then the only way to dissipate the heat is by evaporating water from the surface of the skin as perspiration.