It is completely impossible to be allergic to all perfume ingredients: there are thousands!

 

It is quite possible to develop an allergy (technically a sensitivity but the effect feels much the same) to an individual ingredient: that usually happens after extensive exposure over several years and so most usually happens to people working in the industry. 

It is also possible to be allergic to a particular ingredient (or occasionally a group of related materials), which normally happens from birth or very soon after, though it can be discovered later in life.

Another common misconception is that you are more likely to have a reaction to synthetic materials than natural ones: the reverse is in fact the case.  That is because natural ingredients are made up multiple chemicals (sometimes hundreds have been identified in an individual essential oil or absolute) and so if you are sensitive to just one of those, you'll be likely to get a reaction from every natural that contains that particular chemical.  For example if you are sensitive to limonene, you'll not only react to that indivdual material but also to all the citrus oils and many other naturals that contain limonene.

You can easily see why a reaction to a common chemical could lead you to believe you have an allergy to all perfumes: but if you're making your own (and if you're shopping at Pell Wall you're probably at least thinking about doing so) you can make fragrances, quite successfully, that avoid the material that causes you a problem as long as you know which one it is.