I'm right handed but play lefty, maybe because my stronger arm is my left...go figure. I hurt my right shoulder a couple of years ago and started to play righty for 2-3 months but found I didn't have as much power. The pro at Hank Haney's thought my right handed swing was better than my left, which made me think I might eventually be as good right handed. But I'm about a 4 from the left and maybe a 12-14 from the right on a good day so I'm staying lefty because I frankly dont want to lose the season or so that it would take to switch completely. The pro said it's the same swing from either side; one's just a mirror image of the other, so I'll continue to try to make improvements from the left side. My experience in all this was that the hardest thing for me to do was to square the left hand at impact when I played righty.
Good instruction from a good pro is the key if you decide to make the switch.