do not be worried
eye and hand dominance have nothing to do with shooting well. I am left handed. I started playing right handed when i was a kid, and then didn't play for quite a few years and then for some reason switched to left handed in my early teens. I can still play right handed pretty well, just don't have a big stroke, as long as i roll the CB I'm ok.
Same thing goes for the eyes, I'm right eye dom and shoot left handed.
I switched hit since i was a kid in baseball and never had a problem, shoot a gun boths sides equally well (shotgun, bird hunting...)
Play on whatever side you want to it will not make a difference as to how well you can or can't play. But if your new to the game I do suggest that you develop your other side as it will help your game, and reduce the chances of you having to use the bridge (some call it the crutch).
no worries,
Grey GHost