I feel your pain - I would get dry eyelids from different types of eye shadow. On top of that I have super sensitive skin & trying new products can be a nightmare! Your best bet is to try out a natural, paraben-free, liner that has less chemicals.
I am a huge fan of Kat Von D's Autograph Pencil. It's paraben free & I don't need to use primer to make it stick.
Tarte also has a great one: SmolderEyes Amazonian Clay Waterproof Liner.
I would also suggest switching your mascara to a natural & paraben-free one like Tarte's Light's, Camera, Lashes! because mascara might be a contributing factor.
Hope this helps & good luck! May you never have a problem with eye makeup again