Is there anything to take (pills or anything) that would stop someone's face from blushing when asked an embarrasing question?

Blushing: is part of the normal "fight or flight" mechanism which is hardwired through our sympathetic nervous systems. The capillary blood vessels just under the skin dilate, causing the pink/red appearance. Some drugs, which limit blood vessel reactivity (such as beta-blockers, clonidine) or anti-anxiety medications may help. But much better would be cognitive therapy to learn different responses.