That's similar to my experience. I can get some tension-related headaches to go away by relaxing certain pressure points, which can be done either mentally, manually by massage, or by stretching certain face muscles and the muscles in the neck and shoulders. However, this works better for certain types of headaches than others. If there's a major fluid build-up in the sinuses, I may have to clear that up by eating hot-pepper salsa or something like that, or by making sure I don't sleep in a position that the fluid builds up on one side of my head (for me it tends to drain to the right side, so sometimes I have to offset that by sleeping on my left side). Also, if I miss a lot of sleep I will eventually get a migraine no matter what I do, and even migraine aspirin won't help until I catch up on my sleep. So it depends; but some kinds will go away by relaxing, I find. Some things that help me are: flexing my shoulders and neck in various directions, moving my eyes around in different directions, yawning, and massaging certain points like the top of the skull, base of the skull, under the center of the eyebrow ridge, between the eyes at the top of the nose, the temples, and wiping my palms across my forehead horizontally and then vertically up and down my face like I'm rubbing my cheeks into a smile--smiling helps relax the face muscles :-)
A few years I figured out a why to relax my head just so and make most headaches go away but I have never been able to explain it to anyone. It started when I figured out that I was making most headaches worse by thinking about the pain and sort of tensing up. By reversing that certain types of headaches go away. Not all types but the ones like sinus ones that seem most common for me.
I finally figured out what was causing my headaches. With all the hormones I have going on right now, I get vey emotional. Everytime I stress out, panic, or cry, I get a massive headache that puts me down on the couch or in bed for hours. I can't function when I get a headache these days. Nothing but rest gets rid of them. My tactic is to avoid getting that riled up in the first place.