Why does sleep deprivation cause red eyes?

This could be that you have a small viral infection of the eyes and a bad back, or there is a disorder called Ankylosing spondylitis, which is caused by the immune system attacking the body itself. This is a progressive back condition which can have dry eyes associated with it, although not usually a sudden onset as in your case. There is a blood test that can help to confirm this, so it is best to go and see your GP and discuss this possibility.