Sounds to me more like you consume _a lot_ (therefore have a very strong physical dependence) rather than having extremely fast metabolism.
Alternatively, you might be prone to migraines, and thus are sensitive to headaches of all kinds. That's me, I truly hope that's not you (wouldn't wish that upon anyone).
I promise I don't. I can be on a teaspoon of strongish instant coffee twice a day and it still happens sometimes (though it's worse when I'm drinking more of course). It can happen literally overnight, even when I'm on a steady intake.
The headaches are reliably cured within maybe 20-40 minutes by application of more caffeine, so I don't think they are migraines.
Alternatively, you might be prone to migraines, and thus are sensitive to headaches of all kinds. That's me, I truly hope that's not you (wouldn't wish that upon anyone).