Have you seen a neurologist or headache specialist or only a GP? If there is a cause maybe it can be treated and you can find relief. I do get migraines, but not every day, not even every week. My other guess is allergies, but in any event, keep a good record of what you are doing and feeling, and bring the information to a doctor! I don't think it's wrong at all to post and ask though, you get more ideas and that will help.
Running doesn't help me as much as a vigorous yoga class, the "flow" kind that is more athletic and movement based, then moves to static poses at the end. Or dancing, that works too. The cycling sounds like enough, honestly, anything that is regular and kind of exhausting, will relax your mind.