This might sound strange but what happens if you pee on yourself? Would you be willing to pee down one leg and pour water down the other?
(I am guessing it might cause an unusually bad reaction since it is another way to get rid of contaminants and I would suggest the immune reaction happens as a result of some contaminant, that is produced by your body, when it reacts with water, rather than a reaction against the water.
If the reaction is the same level I would be inclined to think that the disturbance is caused in your skin. If no reaction I would be confused :)

Would you be willing to try a sauna or steam bath just to see what happens? (Probably a bad idea)

Have you tried rubbing a wet skin area on someone else to see if they also exhibit a reaction?

Have you addressed or found a cause for the skin itches you mention?
(I can have something similar sometimes - very dry feelingskin with a firey/scorching itchy feeling, mostly on my arms.)

Do you use/been prescribed any skin creams and do they reduce the rashes?
(I had a "skin allergy" on my legs that became a lot better after using a fat skin cream for a while, even if I still tend to get rashes when exposed to the sun)

You mentioned a "lottery". Do you keep a diary? ie, of what/how much/often you eat, if you expose yourself to sunshine, exercise and the severity of any rashes.

What does your blood works say? Any tendencies towards lowish or highish values within the "normal" ranges?

Have you tried supplementing things like Zink? Tried fasting or low-carb / keto diet (several conditions depend on high-carb diets)?

Any other weird/unaccounted for symptoms?

Thanks for settling my curiosity.