The brain is a very complicated organ of which understanding is still its infancy. Little is known about how most headache medicines act on the brain, other than that they stop pain with no apparent damaging effects. It should therefore be taken with caution when people make adamant statements that alcohol kills brain cells. Long term studies have shown that moderate consumption of alcohol does not kill brain cells, or damage the brain in any way that is not quickly reversible. Studies have even shown that moderate consumption of alcohol can enhance cognitive functioning.
It should be noted that long term abuse of alcohol will cause irreversible damage on your brain, as well as much of your body, and is still a very bad idea.