Actually it may not be a psychological thing. I get hives from pressure on my skin. Putting a hat or helmet on definitely puts some pressure on your hair and where it contacts your skin. Just a thought!
It is psychological with me because it's as soon as I put on any kind of headwear. At least with cycle helmets you can scratch through the vents Honest. There's nothing running around in my hair...really
There are a lot of unwanted, unloved bikes out there - go on give a bike a good home