Here is another vote for Jaipur Homme, both the eau de toilette and the perfume. My skin never turns red or rashy, but I can feel the product making the skin of my forearms feel like I have a slight burn.
My Antaeus and my wife's No. 5 produce mild asthmatic symptoms in both of us. But we love them both, so we put up with it.
As far as something that is just harsh on the nose, Bulgari Pour Homme Extreme. I love this one, too, but the harsh opening note never really goes away on me--causing my nose to kind of burn.
Waaaaa, Waaaa, Waaaa. I know. Stop with the whining.