I actually purchased a naked palette for my grandma although it was the naked 2 basics palette, I think the formulation is all the same. she has very sensitive eyes and she loves it. the shadow stay on a really long time especially with the use of a primer I have had this pallet for about two years now and it is still my go to her use it multiple times a week.
Go to Sephora in JC Penny and ask the girls to sample the shadow for you so you can test it since you have such sensitive eyes. They may test it on you right there. I love UD and I also have sensitivity but haven't had issues with these. Just remember to always use a primer and they will last.
I have a couple of the naked palettes and the pigmentation is disappointing. And I'm very fair skinned, so that says a lot. Other than that they're alright. With some eyeshadow primer it stayed on for me, I've never tried without though.