I get double vision and feel woozy after leaning the back of my head on pillow or couch back. What could be the cause of this?

Low blood flow. In some patients the blood vessels that run in the back of your neck to your brain (vertebral arteries) can be pinched by the spine, especially if you have arthritis. This can cause symptoms when you put your head back as the blood flow to your brain is diminished. It could also be caused by spasms of the muscles themselves. You should start by seeing your primary care doctor and getting an exam.
See your doctor. There are many different causes for your symptoms, some related to the eyes, some related to other conditions. As well, your age, medical history, and use of medications may contribute to these symptoms. The only way to figure out the cause of your double vision is to have an examination either with your primary care doctor or eye doctor.