OP: when does your allergic reaction started?
Are you sure it's due to metals or is it due to something else that you are touching or using to wash your hands?
Don't be fooled by the initial guess.
I will be completely miserable not been able to touch my Mac, allergic to my Mac

!!!!!!!!
So, here is my story:
I had a terrible reaction once on my hands, and since then it happens when the allergen is present again. My fingers get tiny blisters all together forming what I call a "Hellboy hand". They itch and my fingers get swollen. And after several dermatologist visits and trying to find what was causing it, some told me that I was allergic to soaps, and others to nickel in my keys.
I realized that the location of the allergic reaction was always starting specifically on my right hand fingers, thumb and pointer, and not on the left hand.
And after checking what I was doing during some days, I realized that it was due to the liquid hand soap that was used at my employers' restrooms, and also what was the reason why it was always on the same spot.
I wear glasses and I am used to wash them with dish soap at home, and while away liquid hand soap, I do this at least once a day. So I scrub the lenses with my fingers.
And the key reason, besides the soap itself, was that sometimes I was not rinsing all the soap from my fingers when doing that, you know always in a hurry. Now I am very careful with it.
So check what your habits are, and what other things you touch or put on your hands.
Remember that another way to avoid the contact might be using a hand lotion that will keep a protective film between your skin and the allergen. Ask your doctor about it in case you prefer that instead to use a glove or cover your Mac.
Good luck!