Hello. 3 years ago, I developed a skin allergy (eg, got hives and severe itching) to body lotions and washes with "fragrance" or "parfum" listed in the ingredients. Since then, I've mostly limited myself to using Eucerin Calming Body Wash and Eucerin Calming Cream.
However, I am able to use eau de parfum or eau de toilette on my body (behind neck, on wrists, behind knees) without breaking out. And I can use shampoos / conditioners with added fragrance, as well (though my scalp has some sort of mild dermatitis, it is nowhere near the irritation level of my body).
This makes me think that I'm allergic to something else other than fragrance in body lotions / soaps--maybe a preservative or other chemical that manufacturers often pair with fragrance?
It may also help you to know that I can use Dove Beauty Bar and Palmer's Natural Bronze Body Lotion with very little reaction. My skin also gets hives in reaction to topically applied salicylic acid (an aspirin derivative), though I can take ibuprofen (another aspirin derivative) orally without issue.
Diagnosing allergens is very hard and you will need to see a specialist to be able to work this out, or at least eliminate some suspects.
Fragrances are very complex mixtures of both natural and synthetic chemicals and it may be just one compound or family of compounds that you have the allergy to, so while some fragrance cause a reaction others don't.
The reaction to Salicylic Acid suggests that you may have a topical sensitivity to salicylates (Ibuprofin while in the same therapeutic class is not a derivative of Salicyclic Acid/Aspirin). You'll really need a see professional and have some tests to diagnose this.