The information that ANNUK gave you is really what you need to explore. I agree that it does sound like you have CLUSTER HEADACHES, which are excruciating, but they generally don't last more than a few hours at a time. They do usually bother your for several days or weeks, then go away for a while.
I think your problem is that you have unknowingly gotten yourself into a cycle of "rebound headaches", which come from overmedicating yourself. If you are taking Ibuprofen or similar OTC mediation, basically you are creating a cycle of feeding the headache to help the pain, but as soon as the medication decreases in your bloodstream, your body interprets it as withdrawal and the headache returns. This is probably masking the correct diagnosis of cluster headaches. If you are in a continuous cycle of the rebound headaches, you are never going to get a break.
The rebound headache, also called an overmedication headache, is only stopped by breaking the cycle. The rule of thumb is that you never take more medication than recommended, and never more frequently than suggested. You should never take prescription or OTC medication for more than a couple days a week, no matter how bad the pain feels. You have to cut back on the medication, or you will never break the cycle.
Once you get the cycle broken, you could have breaks from the Cluster headaches for weeks or months at a time. Now doesn't that sound better? It's not an easy thing to do, but think how bad it would be if you were trying to kick crack or heroin. Maybe not so bad after all.
Let us know how you are doing.