The list of conditions that can cause headache and fatigue is so long that there isn't much hope of finding the cause unless other symptoms appear to help narrow down the diagnosis, or unless some diagnostic test fortuitously isolates the cause (this can be targeted to some extent based on the relative incidence of different possible causes).
It could be anything: stress, longstanding low-grade infection, depression, neoplasms, brain tumor, sinus trouble, allergies, cardiovascular disease, malnutrition, liver or kidney disease, diabetes, and so on. If the headache varies with exercise, that cranks up the plausibility of cardiovascular issues a bit. The onset of persistent headache in a person with no history of headache also requires investigation, especially in people over 40—a brain scan might be indicated (if the fatigue by chance equates to a change in mental status, this is all the more important). Headache and fatigue are also among those mystery symptoms that sometimes appear to have no cause at all, no matter how many different tests are carried out.
If it never goes much beyond headache and fatigue, about all you can do is treat the symptoms. Mention the exercise thing to your doctor, that might help narrow it a little.
Unfortunately, in order for a doctor to be able to fix something, there have to be enough symptoms or enough distinctive test results to point clearly to some precise cause. Otherwise there's not much more that he can do than you can.
For an aviator, headache and fatigue of unknown cause shouldn't be a problem unless there is a risk that they may become incapacitating. If a cause is isolated, it might or might not be disqualifying (diabetes, maybe; tension, probably not).
I've had headaches ever since I was little. Rarely a serious problem, but a frequent annoyance. No cause ever isolated despite all manner of tests. Aspirin and I go back as far as I can remember.