Yes, I have moved my sites from left to right. This is also what I meant by my arrow and my pins being perfectly centered (when looking down the shaft of my arrow and the sights, the pins are basically centered in the middle of the shaft). There may be some other term for this.
First off what motownhonkey said was right. You said that your missing left, and moved the sight pin from the left to the right. If your missing to the left, you need to move your sight pin to the left, not to the right. You move the pin in the direction of the hit.
Second, your rest could be off and causeing you to shoot to the left. If you haven't had your bow paper tuned that would be a good place to start.