Since you're using System.Drawing you'll need to tell the drawing methods (OnPaint() or where ever you're drawing) to start drawing at an x offset of -10 pixels. Everything you draw would then be offset by that amount.
Shifting the whole drawing left 10 pixels would be cause to invalidate the whole screen region, not just the 10 pixels on the right of the screen. There are a couple of ways you could do this:
1) Set your offset to -= 10 pixels. Invalidate the whole screen by calling Invalidate(). This would force a redraw of the entire screen and, as long as you have coded your offsets correctly, will redraw everything 10 pixels over.
2) Take an in-memory dump of what's on the screen and make an Image out of it. Then redraw that image 10 pixels to the left off the screen. After that, simply Invalidate the right-most 10 pixels.
Method #2 is, in fact, a lot slower than method #1. Redrawing the screen is quite fast if you don't have millions of things you need to draw.