It never donned on me until we moved to California; that heel position is on the wrong side. Having rarely walked on a sidewalk when we lived in Canada; it wasn't until I was regularly walking on pathways and sidewalks that I realized that our dogs are on the wrong side. Heel position is on the left; but our dogs should walk on the right. This is because if we are walking in an area where there are lots of people and other dogs then we walk on the right, so should our dogs. Otherwise our dogs are then in the middle of the pathway and sort of in the way.
I remember when I had my first training client who asked if they could 'heel' on the right. "Of course" I said, not realizing that I then had to rethink everything that was well ingrained in my head. I had to change the finish, the swing and all my hand signals; I had to do everything in a mirror image of what I knew. It took time, I had to think it all through before brining it to them to learn; heck I had to relearn before I could teach it. But learn and teach I did and now I use both sides for Elsa. Why not teach her both? She has more brains than she knows what to do with so she will either heel or right; which is my word for heeling on the right.
She's pretty darned great at it. I have to say that we use 'right' far more than we do 'heel.' I tend to use 'right' when we are out and about in more crowded areas; and let her walk where she pleases when we are at parks and open spaces. Now we have to work on teaching 'turn' on the right side which is again entirely different. When I say "turn," Elsa knows that she must hold back because I am going to turn directly in front of her. With lots of training she knows how quickly I turn and she's on the ball. A turn with her on the right will be the same except that I will be coming from her left going right.
I've been teaching 'heel' since the age of 13; that is a very long time. It is one of the harder things to teach; simply because you must take a great deal of time to get it correct. Once it is taught you can teach heeling on the other side if you like; that or just teach the right side from the get go. A dog must learn where the position is and then to walk and continue to stay there while you move. Then you add in the sit when I stop aspect. There is no yanking involved; that was long ago and it makes me shudder how much yanking we were taught. NO YANKING OF NECKS. I cannot believe how callous many humans have become to neck yanking.
So whether you are a lefty or righty makes no difference as far as where you heel. You can do either, both or none. It is entirely up to you. On a day to day, out in the public world; I would say that the 'right' side is of more use. If you have never taught heel then hire a professional. I always laugh when I see people repeating "heel, heel, heel" to their dog and have no idea what heel really means. Dogs don't come pre-programmed with the knowledge of 'heel."