I found out I was like you by accident. I was in N.C., with a Friend of mine who had to have the best of this, and the best of that, etc. He could afford it. Well he had to have a Browning, Citori, Special edition, over under. Then we went to the local trap and skeet club, and a Champion shooter was there giving lessons. Well I couldn't afford it, so I just sat in the bleachers, and listened to what was being said. I learned a lot just by listening, also how to check for my dominant eye. My left!
I am right handed. Well later on, I tried shooting left handed. I did almost as well as I did right handed.
Just a little bit awkward. But I tried closing my left eye, and did well. I normally shot with both eyes open. It hasn't affected me either way, I guess I have adapted to it over the years. Some people use a patch, or just a piece of scotch tape on the lens of the dominant eye, and it is enough to make the less dominant eye take over. However you want to do it, go for it. Whatever is easier for you, and whatever gets the best results.
Wayne