You may have eczema, which affects the armpits among other places. Eczema is an ongoing condition, which comes and goes. A prescription-strength hydrocortisone would help suppress the symptoms. Choice of antipersperants tends not to matter. You'll need to see a doctor in person for definitive diagnosis and proper treatment.
Take care.
Dr. Rockoff
A related discussion,
Skin Rash on left arm pit was started.
I had the same exact problem for a long time and it turned out it was due to my deodorant. I had been using the same deordorant for 10 years without problem and then one day I started breaking out to the point that I had to scratch and the rash was actually breaking open. I saw a commercial for DEGREE CLINICAL PROTECTION FOR MEN (woman in your case). Two days after I started using this deodorant my rash went away and only came back when I ran out and switched back to my old deodorant. Just hours after applying the old brand of deodorant the rash was back. Needless to say I now keep a good stock of the Degree Clinical protection. I hope this helps you.
I too have experienced a rash under my left armpit a couple of months ago. My doctor told me it that it was eczema and prescribed me a cordisone cream, which helped instantly. The thing is that I never really had outbreaks of eczema (to my knowledge) prior to this year. Is it possible for someone to randomly develop a case of eczema later on in life?
Much appreciated!