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.
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.