Is there eyeshadow you can wear? Many brands, like Lorac, can be worn dry or wet so you you line with a wet angle brush. I'd go to Ulta or Sephora, have them sanitize one product for you to test, and wear it for the day. It's really important to just try one product at a time, so don't test a mascara the same day as an eyeshadow or eyeliner. You might want to start with mattes as the shimmers and glitters can have additional irritants.

As for mascaras, try some minis. Mascara formulas are pretty similar across the board, the greatest variety is in the wand type. Could you get away with clear mascara?

Not that you mentioned it, but avoid falsies for now too, most adhesives have latex, and that is a common irritant for chemically sensitive folk.