There may be some allergens in the water that cause a reaction, and it affects your eyes. Try using filtered water.
Same here! For about 30 minutes after I shower, no matter what, my eyes are puffy and red, and very sensitive. I think it's the chemicals in the water. I live in Florida, so weather doesn't change all that much, but when I lived in Missouri, they would change the level of chlorine and other chemicals in the city water depending on whether it was very warm or very cold. I could always tell when the chemicals increased.
Are you able to open your eyes underwater in a swimming pool? I can't at all, and I wonder if some people's eyes are just more sensitive to chemical changes than others.