Free and Clear has sodium lauryl sulfate. It might be a good option if you are not allergic to sulphates or not concerned about the effect of it being an eye irritant.
The other option to look into is "
Earth Friendly Products Ecos Liquid Laundry Detergent, Magnolia & Lily", which is Sulphate-free, Phosphate-free, chlorine-free, enzyme-free, dye-free, and free of petroleum ingredients.
Good luck
Allergy General