Consider other causes of armpit rash. These may include allergies to food and medication, poison ivy or poison oak, insect bites, or an autoimmune disorder such as psoriasis. Viruses such as flu or chicken pox can also cause rashes.rmpit rash can be the result of a perfume or deodorant you are wearing, a soap product you are using, or even the clothes that you wear. If you experience armpit rash, learn how to recognize and heal the condition. Symptoms might include itching, rash, darkening of the skin, flakiness, pain and increased odor.