I found it helped to put a nude cream eyeshadow (or concealer or primer, if you find one that isn't irritating to you) on the eyelids before the shadow. It seems to act as a barrier.
I had good results with Stila shadows. I think they're a little...oilier?...than most. Anyway, they go on silkier, which helped. I found that the finer the texture of the shadow, the less likely it was to irritate -- but if there's a specific ingredient you're allergic to that might not hold true for you.
I found Urban Decay was the worst, although that might be due to the glitter in a lot of the shades.
Reddish brown hair, pale warm-toned skin with freckles, green eyes.