I would sometimes feel my underarm deodorant/antiperspirant burn. I am a guy, so it was not because of shaving my armpits. It started to get a little worse. It would burn and then itch. I looked online for deodorant for sensative skin. I learned that things such as aluminum in the antiperspirant might be causing me some problems. Plus, there was other stuff that would then burn my already irritated skin.
Deodorant is not antiperspirant. And antiperspirant is not a deodorant. If you are not worried about sweat under your armpits, you do not need an antiperspirant. However, everyone needs a deodorant. Bacteria lives on our skin, and it multiplies rapidly in warm, dark and moist areas such as armpits. You cannot and should not try to eradicate all of the bacteria. If you did do that, then yeast would grow more and you would still stink. It would just be a yeasty stink. A deodorant can mask the stink or keep the bacteria and even yeasts in check.
You can get a deodorant that is made of safer natural ingredients. You may have to try a few to find one that works perfectly for you. I hit on my new favorite on the first try. It does not have any antiperspirant in it, and it smells very good. I have been using it for a few months now. I never sweat a lot under my arms anyway, so it works well for me. If I did, I would just try a better antiperspirant that does not use aluminum. There are alternatives. People with sensitive skin need to try different personal hygiene products that do not cause irritations. You use this stuff every day, so you are irritating your skin every day. It is better to get something that does not cause you any irritations.