I highly doubt it is a reaction to the baking soda. So doubtful that i will volunteer to stand on my head and eat my shoes if it is. A reaction to topically applied baking soda is a topical one. I would suspect a contaminant in something. That is if these two people dont know eachother or about the others 'reaction' and if in fact there were any swollen lymph nodes. As someone else suggested, perhaps plugged glands or pores or maybe a local bug going around and they just happened to stop using the deodorant around the time they were getting it.