Don’t assume ‘natural’ or ‘organic’ are best. Just as people can be allergic to pollen or nuts (naturally occurring substances), they can also be sensitive to fruit or herbal extracts or oils and other plant derived materials and perfume/oils.
Perfume and preservatives are two of the main culpirts in causing skin irritation or allergic reactions. Natural and organic products may be preserved with essential oils or perfume blends which have a natural preservative quality so 'preservative free' does not mean guaranteed irritation free! Other natural preservatives are usually 'systems' i.e. more complex mixtures of ingredients to achieve the same effect as a synthetic preservative. As we say above, the fewer ingredients, the better for sensitive skin.
It is worth mentioning also that may preservative ingredients which are 'demonised' e.g. parabens are actually synthetic reproductions of naturally occurring substances.
Where possible, ask questions and ask for samples before you buy!