I think possibly it’s the position of your head when you read that could be causing this. Is your head in flexion (chin down)? Try reading with your book, kindle or whatever on a book stand, so that it’s facing you, at eye level, see if that makes a difference.
Head in flexion can cause cerebro spinal fluid flow ‘obstruction’ problems which can lead to raised intracranial pressure, causing headache (especially occipital headache, low down at the back), also eye pain and it could interfere with the trigeminal nerve too.
Regards
Barbara
(UK)