It is not as uncommon as you would think.  You should try to shoot with both eyes open which will be sighted primarily with your dominant eye.  Which is your dominant eye?

ditto what 1GUNRUNNER said. You should train to shoot with both eyes open.
There are 2 major reasons for this.
1. You don't lose your depth perception
2. In an actual gun fight the last thing you want to do is cut your peripheral vision by 50%.
Especially in a low light condition.
I to am right handed/left eye dominant. I shoot handgun with both eyes open and have been training myself to shoot service rifle left handed. It wasn't as hard as I thought. After 20+ years shooting right handed I can shoot just as well left handed after a few months. The sight picture is incredibly clear with no eye strain.