If by left-handed you mean that you carry the yarn in your left hand but still knit stitches off the left needle on to the right, then I'm guessing that you wrap the yarn around the needle in one direction when you purl and in the other when you knit. That would cause fabric produced flat to look different from fabric produced in the round.
Both knit and purl should be wrapped counterclockwise in conventional Western knitting. Many left-hand-carry (referred to as Continental) knitters wrap the 'wrong' way when purling because it's easier. MUCH easier. They either compensate by knitting through the back loop to untwist the stitch on the next row. or go through life happy with fabric where alternate rows of stocking stitch are twisted.
When knitting in the round, though, you are no longer alternating between knit and purl. So either you don't twist-untwist or you're suddenly confronted with fabric that looks the same from row to row where what you produced in the flat has alternate rows of twisted stitches.
If, however, you mean that you knit stitches off the right needle on to the left one, I find it so mind boggling to contemplate that I can't venture a guess on which direction anything else should be done.