One of the complications of shaving your underarms is that the hair in that area doesn't grow in just one direction. The secret is to shave in a "T" shape. Start at the top, then shave down through the middle of your underarm. Then shave across the whole underarm from one side to the other. It helps to pull the skin in the area so it's as flattened out as possible.
Contrary to popular belief, frequent shaving does not cause the hair to grow back thicker or coarser. Certain deodorants or lotions may provide the opposite effect, softening underarm hair and causing it to grow back lighter. So shave as often as you need to, but remember the "T" formation.