i found out about a few years ago that i have become left eye Dominant. after i bought my Longbow i got a little worried as to wheather i needed to buy a left handed bow.
But i heard somewhere maybe on You Tube about keeping both eyes open as Hitman has mentioned and that helped me A Lot.
i have thought of tring to shoot left handed but i'm going to continue shooting right handed with both eyes open if at all possible shooting left handed would seem weird and im not sure i would have the same amount of pull. But thats just me.
best of luck.