If I apply pressure to a certain part of my neck, my left eye goes blurry. Is this from lack of blood in the eye?

Stop pushing. The ophthalmic artery is the first branch of the internal carotid artery. If you press just to the outside of the windpipe, where you feel a pulse, you are pushing on your carotid artery. This also supplies blood to the brain, and if you press on a certain spot your heart rate and blood pressure may suddenly drop. So, you are probably obstructing blood flow to the eye. Not a good thing.