My head pressure has been going on for 5 years, and like the OP, eating and exercise have a definite effect. It seems that "during" the eating process, my pressure lessens and I tend to feel a lot better. about 30 minutes AFTER i'm done eating, however, the pressure comes back a lot worse. It seems that a "busy" digestive system--after a large meal, for example--makes the head pressure worse.
Similarly, if I'm doing strenuous exercise such as running, the pressure becomes almost unnoticeable, but once that grace period goes away, it comes back with a vengeance. After strenuous exercise it almost starts "throbbing" it gets so bad.
So I avoid rigorous exercise these days and just go with long walks, it doesn't seem to aggravate the head pressure like running does, and I do feel better for a while.
I don't think mine is caused by anxiety even though I'm an anxious person. The reason being I have lots of other symptoms that go along with the head pressure: IBS-C, visual problems, worsening fine motor skills, odd gait, lessened skin sensation, intense brain fog and fatigue, etc etc
Pelonis you and I may have a similar case, please keep in touch and let us know what the neurologist says. I'd also get an MRI of the head in your case.