I'm an old man (72). I am strongly right handed and left-eye dominant. I've been shooting shotgun right-handed because that is the only way that feels natural. I tried left handed for a while and it was so awkward, I gave it up. I shoot from the low gun position and track the bird with the muzzle while raising the gun and keep both eyes open until just before the stock hits my face. I then squint my left eye and it works pretty well.
That was the way I was shooting my bow, because I thought it would be too awkward. The difference is that the shotgun has to be continually and smoothly moving - the bow not so much. If I shoot right handed with the bow I have to close my left eye. Or, if I aim with both eyes open and then close the left eye, I will be 8 - 10" left and have to move it over before releasing.
I finally committed to shooting left handed for at least a month to see if I could adapt. Took less than a week. My accuracy is no better than shooting right handed with my left eye closed, but it is so much smoother and faster. I still shoot at least a few right handed and draw a bow right handed as many times as I draw left handed just to keep my back balanced.
I had to drop to a lower weight left hand bow at first, but now I shoot the same weight bow from either side.
If you decide to switch, give it at least a couple of weeks and the change will not be particularly difficult.