I ride left handed for the traditional reasons and start all of my students off using their non dominant hand. It leaves your dominant hand free to open gates, throw a rope or grab the horn when on a cutter.
In showing, it doesn't matter which you use, it's all personal preference. I've never seen a judge ask nor have I asked myself for a rider to use a particular hand. Now if you were to switch hands mid-stream during a class, in most that will be a DQ (especially a trail class working a gate!)
Life is like a camera. Focus on what's important, Capture the good times, Develop from the negatives and if things don't work out, Take another shot.