Some headaches are related to eye strain but it is usually not associated with burning. If rest does not help, see an ophthalmologist.
Dr. O.
You may have "dry eyes"; i.e., inadequate tear production. Dry eyes are a common condition. If you check Dr. Hagan's profile, he has provided some very informative information about this. There are a number of discussions in the forum archives as well.
Have you tried artificial tears? There are some excellent preservative-free brands on the market. If you've tried this and still don't expereince relief, it's probably time to see an ophthalmologist for an evaluation.