Hmm … those are unusual questions

To the more conventional questions … yeah, I don’t see it being a contact allergy either. The very different materials causing the same result, and the fact that no other part of my body seems to be sensitive to them, would seem to point away from that.
The second option, that area and likely other area’s on your body are sensitive? Do you bruise easily? Are you fair skin or is your skin sensitive to other things? Do you have veins close to the surface? When you get bumped, slapped, sunlight etc?
I don’t bruise particularly easily or have unusual skin problems. I am very fair skinned, though given that, not as sensitive to the sun as you’d expect.
And I don’t remember this question being asked, are you playing the thing correctly? Are you using too much pressure? If you can play two octaves easily, you are probably relying on air and not pressure.
I can play two octaves pretty easily. I don’t think I’m using too much pressure - paid attention to it once this started happening, and it’s hard to see how I could use any less and still get sound.
Now to the weird ones
Though its hard to see why I would develop psychosomatic symptoms only after a couple of months …
Do you play any other rim flutes besides quena?
No - I’ve thought about trying some, but at the moment that doesn’t seem terribly cost effective, given the situation 
How did you find out about the quena and was it an instant attraction?
Don’t remember exactly. Yeah, it looked interesting, and at least theoretically, easy to make.
Tried it, and I love the sound and how responsive it is.
Are there any cultures that you are interested in besides your own?
Sure, always been interested in current and past cultures of the world.
What is your ethnic background?
Northern European.
Do you have any other mysteries body pains, rashes, twitches that are unexplained?
No.