I haven’t totally eliminated caffeine from my diet, but I had to quit the coffee because it was just totally killing my gut. I still enjoy my iced tea or even a cup of tea, but tea never bothered my system the way coffee did. But neither is an every day thing and the lack of has never caused me the headaches.
I skip days of caffeine if my headache isn’t so bad and drink herbal teas or just big bottle of carbonated water.