Your underarms are ticklish for a reason: The skin is very sensitive. It's OK to shave, but be careful -- shaving can cause irritation. Razors can nick or cut the skin, causing inflammation, and deodorant or bacteria can further irritate skin.
It's fairly simple to avoid a rash or infection caused by underarm shaving. Use shaving cream to ensure a smooth shave, and make slow, short strokes so you won't damage the skin. If you shave at night, wait until morning to apply deodorant to avoid further irritation [source: Prevention Magazine Health Books PLEASE LINK TO LMI].