Wow, there are many people that are righty and left eye dominant. I thought that I was a rare case. Fortunately, I had a firearms instructor that made the whole class do the thumb test and the triangle test to see which eye was dominant. So right out of the gate I knew that I was left eye dominant.
I shoot with both eyes open with no problems whatsoever. When I shoot a rifle, I shoot right handed but closing my left eye allows me to focus. And most of the rifles that I shoot with have optics anyway.
Try both eyes open, and make sure that you bring the handgun up into your sight range instead of leaning your head over to the side.