Lol. Most humans assume everything that doesn't have a common, socially-accepted explanation is psychosomatic.
If you have any chronic condition that affects your ability to function(surprise, most of them do), 80% of people out there will just cheerfully gaslight and abuse you without batting an eye.
It's "immune mediated", meaning that there is indeed a response by the immune system. Unsurprisingly, histamines and other inflammatory markers are detected. Sometimes anti-inflammatories can help.
I very rarely get itchy after taking a shower. It seems to be related to the level of humidity in the air wherever I am, and also time of day. It's very weird, and I can't imagine how annoying it would be to have that happen every single time you encounter water.
It’s not an actual allergy, more like a water-induced itching, and yeah everyone you talk to assumes it’s psychosomatic, which kinda sucks.