Some good tips above, but here's my own experience:
Do you wear any kind of cycling glasses?
I used to get fearsome headaches when riding, right between my eyes just like you.
Then I picked up a fairly inexpensive pair of Ryders sunglasses (just a light yellow tint)
that seems to have solved the problem right away.
I think it was perhaps cutting out the wind (rather than blocking the sun) that did it.
(Mind you it could have been coincidence, but I refuse to ride without them now)
They're also great for keeping bugs/dust/grit out of your eyes.
Just find something that is a nice fit.
e.g. this is the brand I ended up buying
http://www.ryderseyewear.com/products