I've struggled with this for a long time too and noticed that it's not one specific ingredient that's the culprit, but their combination. My skin reacted fine to perfumes with simple floral compositions like rose or peony, but complex fragrances with amber notes or synthetic ingredients would make it red immediately. My advice is to test each new perfume for several days in a row on the same spot to figure out if it's actually the one causing the problem, rather than just happening to land on your skin when it's already irritated.
Switching up how I apply it also helped - I started spraying perfume on my hair and clothes instead of my skin, and the irritation went away completely. The alcohol evaporates faster and doesn't stay on your wrist as long. Or try applying it to the inside of your elbow or behind your ears - the skin there is thicker and less sensitive. And you can slightly moisturize your skin with cream before applying it, which reduces how harsh it is.