It's possible to get a rash in the armpits from Candida. I was told an awesome trick for getting rid of any rash from Candida (fungus). Use some vinegar (white or cider, it doesn't matter), but be sure to dilute it. Keep the diluted vinegar in a covered container set aside for this purpose, as you do not need to throw out the diluted vinegar after using it. So, it won't take a lot of vinegar to try this. Using a clean washcloth, gently dab any rash caused by Candida, then let your armpits dry out thoroughly.
Do not apply any more deodorant, and never ever use antiperspirant.
By the way, since Candida is my own issue in this regard, using the diluted vinegar has actually gotten rid of the body odor caused by the Candida--all without the need for any more irritating deodorant. So, I believe that the diluted vinegar has a natural deodorant effect even if one doesn't even have a rash.
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You may need to first be sure that you're not dealing with an allergy to your deodorant first. Using hypoallergenic gentle soap in your shower, thoroughly shower, so you can remove all traces of your deodorant. Also, take an antihistamine, such as Benadryl orally. You can also use Benadryl cream on the rash itself, which you may want to try during the daytime as Benadryl is rather sedating. But, you can take the Benadryl at night time which should actually help you sleep--understanding how hard it is to sleep with a very irritating rash in such a place.
DO NOT USE any deodorants or antiperspirants while you are dealing with this rash.
If it is a combination of allergy and Candida, the vinegar solution will take care of any body odor issues.
When it is time to try deodorant again--DO NOT USE any with fragrances or aluminum. Try a natural variety. You can also look online for homemade deodorant recipes.
It could be that your applying too much deodorant and its getting clogged in your pores. The possibility for left vs right is the differences in the amount of sweat. Also it tends to happen more often with a solid stick rather than a gel type deodorant. Decrease the amount of deodorant you are applying and if that doesn't help shop around for other types of deodorant. I hope this helps.