ahhh, this problem.

there is a way to overcome this.
its like practice your brain. play FPS games
daily and when it starts to get a bit dizzy stop
for 5 minutes and stare away from the screen.
go focus on green grass or something else.
alot of people force themselves playing FPS
will lessen and eventually will not get
headaches anymore

first, you must understand what causes the headache.
it is caused by the brain. when you're playing FPS games
your eyes telling that you are moving. while your other
sense telling that you are in a static position. so the brain
is confused which cause the headache. practicing will overcome
this problem. or you could just disable the "weapon bobbing"
to lessen the effect.

a fine example i can take is by big bro.
he suffer headaches when playing FPS games.
because of Gears of War, he force himself to play
and adopt until the headache is gone