The most likely cause for this is pH imbalance under the arms.
The good news is, there is a quick and easy solution!:
1. Mix 1/2 part apple cider vinegar with 1/2 part warm water
2. Apply under your arms and let dry for 15-30 minutes before washing it off.
Applying before getting in the shower is a great time.
The mixture should provide at least some immediate relief of the irritation or itchiness; and is usually is effective for rebalancing your pH levels as quickly as 1-3 days (though for some people it can take longer).
If this doesn't work, you may have sensitivity or allergy to an ingredient.