One simple way to minimize skin irritation (whether it's from an antiperspirant, razor burn, or simply a predisposition to having sensitive skin) is to keep your skin hydrated. Moisturizing skin on a daily basis protects it from the harshness of your daily life, decreasing its scaliness and increasing its softness. When it comes to caring for underarms it's best to apply lotions after shaving and before applying antiperspirant.
Moisturizers come in a few different types which work in different ways. Emollients, such as petroleum jelly, trap water in your skin, whereas humectants, such as your daily hand cream, attract and draw water to your skin from the air. Dimethicone-based moisturizers soothe dry skin through silicon-based polymer technology, and are successful in treating -- or decreasing -- underarm skin irritation, too.