Welcome, from a fellow musician. Glad to read your headaches are lessoning. Are they any better/worse after practicing? I know the flute doesn't take much pressure, but we've been discussing Valsalva manuevers/straining and cerebral pressure on the CCVI thread. My husband's a trumpeter, and he's started making the connection.
Some relaxed, counted breathing exercises with an open throat might relieve some tension. Just a thought....
The playing of high-resistance wind and brass instruments such as the oboe, bassoon, French horn, and trumpet has been associated with increases in intraocular pressure and greater incidence of visual field loss. The Valsalva maneuver associated with high-resistance instrument playing is thought to be responsible, because it causes a rise in intrathoracic pressure and compression of the intrathoracic venous system. This leads to vascular engorgement, increased choroidal volume, and a rise in intraocular pressure. The cumulative effects of long-term intermittent intraocular pressure may result in glaucomatous damage.