I'm left handed, but right eyed. I have to close my right eye when I shoot pistols, rifles,and machineguns iron sighted to be on target. The only way I can shoot with both eyes open is with red dot and reflex sights. I have heard you can retrain your weak eye to be dominant, but I have never know anyone to be able to.
I would not sweat it. Just spend time training on the basic fundimentals such as trigger sqeeze, breathing, sight picture, grip, and malfunction resolving such as SPORTS.