Terry's advice is good.
In addition to what he said, realize that hitting to the right when shooting left handed is the equivalent of hitting to the left when shooting right handed. There are many, many reasons why this could happen.
You eliminate one of those reasons when you cover your right eye, which probably is your dominant eye. You should test yourself, BTW, to verify that this is true. If you happen to be left eye dominant, you don't need to cover your right eye,
The next 47 or so reasons can all be lumped under “form” which is how we shoot the bow. Eliminate these reasons by getting some coaching.
The dozen or so reasons beyond that can be linked to equipment, which means that your arrows should be tuned to hit where you are looking.
However, you can save yourself a lot of trouble if you make sure, from the start, that you are anchoring your arrow directly under your left eye. If you are anchoring your arrow to the left of your left eye, which is easy to do, you will miss to the right.