I don't know if our brain can recreate smells as well as it does sounds and images, but certainly, it can identify and distinguish dozens, if not hundreds, of smells when exposed to them. Just think about food - without realizing, we instinctively know what smells like what. But identifying smells in perfume is difficult because we've not consciously been exposed to them in isolation. The first step in a perfumer's school is to learn how each material smells. Then one can start combine them and learn accords, which, sometimes, the nose cannot perceive as separate combinations of smells, but as accords. But to do so one has to exposed to the materials - and these learning kits can be expensive.
Then, of course, I'm sure to be a top perfumer one needs some special talent. You evidently have a special talent for music. But, even without a special talent most people can learn to analyze and enjoy music - and the same is true of perfumes.