Alcohol works well. Time will get your underarms back to their right color. I tried baking soda once. It burned and turned my skin red and it took over a week for the redness to go away.
I don't know about whitening but plain old alcohol will stop underarm odor.
I am allergic to commercial deoderants and have found that cleaning my underarms with alcohol after shower and before I leave the house works very well. After all bacteria are what causes the odor and alcohol kills bacteria.
It sounds like your skin might be irritated by the baking soda. Try using a mix of two parts corn starch to one part baking soda and see if that helps. If you still have a reaction you could try using corn starch on its own, too.
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