I kind of messed up early on when I first started too, and now I've finally decided I need to try to correct it somewhat.
Basically, I'm right eye dominant, but I've been shooting lefty since I was very young because that's what felt natural (I also write left handed, BTW). It also helped that my right arm is my strong arm and it is much easier and far less awkward to use it to support a long gun while I use my left hand to manipulate the trigger.
However, shooting this way usually means I have to close my right eye to obtain a good sight picture, or I have to mentally force my left eye to become dominant for those few seconds. Not too big of a problem for most cases, but it slows down target acquisition by a hair.
The upshot of this is....with pistols, I'm completely ambidextrous. I suffer no accuracy loss when switching from one hand to the other. With long guns, its not a matter of accuracy but a matter of comfort. Using my left hand/arm for support instead of my right just feels awkward. I'm trying to train this out, but it might take a while.