I am a "lefty" turner, but I have learned that I need to be able to turn both right and left-handed. I always teach my students (who are, of course, mostly right-handed) to turn both ways - you just can't do it all in only one direction. What I have found is that we lefties have an advantage - we are usually forced to use our right hand for more things than rh people have to use their left, so learning to do things both ways usually comes easier to us!
This is the time to learn switch-cutting, now when you are a beginner. You will find it opens up a lot of possibilities that others who can't turn both ways just don't have.
"Keep those shavings flying!"