Years ago while doing my OB rotation as a nursing student I developed an axillary rash after shaving. It got really ugly and spread, and my theory was that it was a staph infection I must have gotten from a baby in the newborn nursery. I figured I was holding or feeding one of the babies and s/he was breathing bacteria from his/her nasopharynx into my irritated armpit, where it was nice and warm and moist. I treated it with OTC triple antibiotic ointment and it went away quickly.
The other experience with underarm rash was my husband's. He came to me with a flaming red bilateral rash extending down his sides and asked if I knew what it was. It took me about 30 seconds to figure out he was having a reaction to his deodorant.
A fungal infection is probably a good guess, so if you want to self-treat you could try clotrimazole like the other poster suggested (I would use cream). You should see an improvement pretty quickly if you're on target.