Be wary of products that are labelled "fragrance free" or "unscented" as these terms may not necessarily mean they do not contain fragrance chemicals, they just imply the product has no perceptible odour. These products may possibly contain a masking fragrance that is used to cover up the odour of other ingredients.
Note that clothes washed in scented laundry detergent can be a problem with prolonged skin contact of the garment in the presence of moisture and heat. It would be best to use fragrance-free laundry detergent.
Alert your doctor or dentist to the fact that you have an allergy to fragrance mix. If you are highly sensitive, your doctor may also recommend a special diet that eliminates foods to which these allergens or related allergens are added as flavouring.
Your dermatologist may have further specific advice, particularly if you are highly sensitive to fragrance mix.