At some time or another, the majority of people get that painful, red mass in one or both of their arm pits. This is called an abscess and it came about because a sweat gland got blocked or it is a boil, which is an abscess infection that forms around a hair follicle.
Common causes are your deodorant plugging your pores (consider changing your deodorant), extra heat generated that opens the pores and something gets clogged in a pore, or it simply can be an infection from bacteria build-up in the area. You can still exercise while you have this problem, but don’t think it will go away on its own.
An abscess needs to be treated or it will get worse and can cause blood poisoning. The best home remedy for this is putting a hot (not burning to the touch) compress on the affected spot 4-6 times a day and the problem should go away in a couple of days.
What is a compress? A simple, inexpensive one is to wad up one full size paper towel, run water over it, squeeze out the excess, heat it up in a microwave for 10-15 seconds, and then place it over your abcess(s) until the heat is gone.
If it does not cleared up in 2-3 days, go see a Dr. to lance it, drain it, put you on antibiotics, and then have you check the area, clean it of drainage, and sterilize it with alcohol or Listerine until it heals.
For other tips where Listerine is really helpful, see my book MAX Out the Army, navy, Marine, and Air Force Physical Fitness Tests.