No, I think you have eczema, nothing internal or infectious. Try over-the-counter 1% hydrocortisone and moisture lotion twice a day each while you wait to see a skin doctor for definitive diagnosis. Eczema comes and goes, so you'll want a prescription to use from time to time, but antiperspirants just make it red and don't cause it, so you can use anyone you want.
Best.
Dr. Rockoff