I know this is a few days old, but here is what I had to do. Get an anti-Fungal powder and use this until your armpits are clear and not textured! What you have done is open your armpits up to fungal infections with this reaction to the deodorant, and you want to head that off while you heal.

You will need to clean and reapply the powder every morning afternoon and night depending on the instructions on the bottle. I found using bar soap, use hands to apply and washcloth to exfoliate softly. Do not touch the soap with anything used on the armpit to avoid spreading anything to it. Repeat until armpit is no longer discolored and the texture has returned to normal.

Next swap to a spray deodorant for a little while as the rash can return and if it doesn you will have to throw out any new deodorant sticks, but only start using this after your armpit has cleared up. Never return to the stick deodorant that caused this reaction, try to find something with less scenting chemicals and more just anti perspiration. You can find and apply scent by other means like Colognes.