No, although the "pathways" of vision do move through the left and right sides of your brain. The visual cortex is located in the occipital lobe in the back of your skull. The left side of your brain controls your the right fields of vision in both eyes and processes information received from it (it controls the right field instead of the left because the information from the eyes crosses in the place called the optic chiasm near the middle of the brain, and because the retinal image is inverted). 
