You are trapped on a frictionless sheet of ice. If you trued to escape by blowing, you would have to inhale eventually, which would counteract the force you gained by blowing. However, if you were to turn your head and inhale facing the east, you would gain some force moving east. If you then turned your head and exhaled towards the west, you would gain more force towards the east. You could use this to build your speed eastward.
Is this correct, or am I missing something?