I think bad eyesight can cause headaches and dizziness. The extra-ocular muscles play a very important role in the process of vision. Extra-ocular muscles are responsible for the movement of your eyes. These muscles can let you look up, down and sideways. They can respond to orders of your brain.
Bad eyesight could be related to your headaches and dizziness. Absolutely, when you strain your eyes and squint a lot to see something, it can lead to headaches and nausea. The reason is that the frontal muscles are straining and then causes headaches. It could be nothing but it can be a sign of something more serious. Seek a doctor if you can't handle with this. Hope this helps!