I have used Secret Clinical Strength - Sensitive unscented for a long time.
I really like it, and it seems to work well!
(no redness or itching, etc.)
I can also have sensitivities. And I actually don't like the idea of armpits that smell like peach-blossoms or old spice.
Something about the combination of hot armpits and these scents is, like,

And, I def. don't want anything that would clash with my favorite perfume.
DH showers and puts on antiperspirant before bed, and I had to get him to go 'unscented', because I would lay there beside him, and be breathing and smelling that stuff!!!
I actually like the Axe scent my son uses!
I think his girlfriend says she loves it.
I have used shampoo's, even some of the good more expensive ones, that leave my scalp and back itchy.
The Pureology NanoWorks is the best shampoo and conditioner that I have ever tried. And, no sensitivity!