You must have unnecessarily sensitive skin
Some of the deodorants are pretty strong. Mennen, Degree, etc. Some roll-ons. I noticed that on the containers of some of them, they warn against the possibility of kidney damage if you have any kidney disease. Particularly strong are the ones that come out as a solid bar when screwed up, but go on as a semi-liquid. They irritate my skin, even to the point of skin cells dying and sloughing off. If I use them(as well as some roll-ons) I have to make especially sure that I allow(or cause) them to dry before I put on my undershirt.
I found the ones that smear on from the container as you rub(though unsightly)to be the mildest. In my opinion though, they are not as effective as nor do they carry as powerful an odor as the others. If I am using one, I might use cologne if I want a certain presence or on certain occasions.
I don't care at all for spray deodorants. Maybe there are good ones, but I haven't found any that appealed to me.