Are you putting any thoughtful of face cream on your face. If you are when you sweat it will be coming bad with your sweat and going into your eyes. You got to take heed, there are so many chancy chemicals in skin care currently.
Because sweat is acid that kills germs on your skin. I've never been stung by sweat before tho, conceivably you should check with your doctor about it!!.
I think it have to do with the ph level... that is to say the acidic and non acidic horizontal. and it is not just the salt beacse tears already hold salt in them
You call for to seek medical help..
Answers: Sometimes it does.It depends on the ration between salt and water.
Sometimes you will have a difficult percentage of salts like magnesium chloride to hose, this will sting on release with the water.
To avoid this, drink plenty of river. Stinging sweat is often a sign of de-hydration so have for a moment salt with your dinnertime and plenty of fluids...(i.e. water)
ADDITION - after reading your adition, I think I might know what it is.
As I have said above, it is a mixture of waters and salt. As the sun evaporates the water (as its evaporation point is lower than salts) it makes the salt more concentrated, which might lead to irritation, especially with the salt based on Group 1,2 metals (like sodium, magnesium, calcium) etc.
when you sweat, brackish water is released. in strong sun this saltwater is dried up and the brackish that is left over pinches your skin. it's approaching if you come out of the sea in really hot weather :D