How common is it to get scalp swelling from bleach?

Not uncommon: Depending on how concentrated and how long the application was for, swelling would not be an uncommon side effect. Some people with sensitive skin may be especially vunerable.

Allergic reaction?: Are you applying bleach to your hair to lighten it? Is it specifically made for hair? If your scalps swells up, is itchy or painful to touch, you may have had an allergic reaction to something in the bleach you used. Stop using the bleach, wash your hair out thoroughly and watch it get better.