Your avatar shows you shooting a rifle. Looks like you're shooting with your right hand. 
You should train to shoot with the hand that corresponds to your dominant eye. Over time you will be able to develop skills to shoot with either hand, but in high stress situations, you will find yourself reverting to your dominant eye. Over the years I've trained many students who are "cross eye dominant". Most people tend to do better shooting as I previously explained.
With handguns, it is possible to shift your body position and use your dominant eye to shoot, but with rifles, you will need to use the same hand as your dominant eye. It's nearly impossible to adjust your body to look over the barrel and line up the sights.
For simplicity sake and in your best interest, I strongly recommend finding a gun you like that you can shoot with your left hand. It will feel odd at first, but with practice, you will get the hang of it. As you already experienced, you shot better with your left hand. When shooting long guns, shooting left handed is critical.
Good luck in finding a gun that you like. There are many production arms on the market that are easily adapted to left and shooters. I recommend you shoot as many handguns as possible to find out what will work best for you.
gf