I had the darn things for years. I understand about the rebound headaches.
I even went to a headache clinic in Ohio. Finally during a routine test they found out I had byjimanee, (spelled phonic) an irregular heartbeat, something that is often missed. Doctors put me on Verapamil, 240mg once a day. My headaches stopped. Just like that. I sometimes get little headaches, but doctor told me the brain is 80 percent water and does not like to be dehydrated so drink a full glass of water when I feel headache coming on. I was on Darvon, Darvocette, Empirin 3, and sometimes had to go to ER and get shot. Not been there for ten years now.
Doctor told me that in his experience a headache was a symptom of something wrong in another area of the body. Once you find what that is, your headaches will stop. Trouble is most Doctors think a headache is a little thing and don't even look for cause. They also told me to stay on a routine. Get up the same time each day, even your days off. Do not sleep in. Eat a good breakfast. Go to bed at the same time each night, try to get 8 hours sleep. Sound boring and not easy to do, but is worth it. Mine were so bad I thought about ending my life. Thinking back I realize, that just like that, was more like a month after the Verapamil, and I was off all other meds too. Also check your blood count. anemia can cause headaches.
Hope this helps.