SciMMiA, your English is excellent, but I'm not sure I completely understand everything you have written. As Bejeeber says, the long duration of your primary attacks does not sound like it is CH, but the fact that a triptan helps, and the eye/nose symptoms, suggest that it is at least in the same category as CH. Are you also saying that in addition to the six bad attacks per month, you also have some "small" pain every day, and that pain is mostly associated with your eye?
If you do have CH, then you should have oxygen, and you should probably have a triptan that is not a pill but is either an injection (called Imigrane in France, I think) or a nasal spray (which I think is called Zomig in France). These triptans will stop your attack much faster than a pill, and if you are only using them for attacks about six times a month, you should tolerate it okay. Oxygen will stop a CH attack pretty quickly and it is not as potentially harmful as triptans. Oxygen is inhaled through a mask, coming from a tank/cylinder/cannister. Oxygen and triptans are the recommended treatments in the European Union for stopping a CH attack. Verapamil is the recommended medicine for preventing attacks. You have to take it for several weeks before it becomes effective, so you don't really know yet. Your dosage is in the low range, so your doctor might be going to increase it. That is the way that verapamil is correctly prescribed, starting with a somewhat low dose, monitoring for side effects, and then increasing as needed. Some people need three or four times as much as you are taking before verapamil is fully effective. You could also try the CGRP drug Emgality.
As Bejeeber has said, the Vitamin D3 regimen and busting are often very helpful for a variety of conditions. They have fewer side effects than the medications I listed above.
There are some people here who have both migraine and CH, sometimes at the same time, or one directly following the other. This is a possibility. Another possibility is some kind of hemicrania (hemicrania continua (HC); paroxysmal hemicrania). These look a lot like CH, and HC includes a constant headache. But . . . usually they do not have such long-lasting attacks as yours, and usually they do not respond to triptans. Have you seen an eye doctor to rule out a headache associated with an eye condition?