Great reply from Pebbles'. The reason a concentrator is ineffective is that it makes O2 from room air, and it is not 100% pure O2 (there is still some room air mixed in). Plus, the regulators on most concentrators don't go up to 15 lpm (liters per minute), which is where you want to be. I'm telling you all this because it's likely that the O2 supplier has no experience providing O2 to someone with CH, and you might have to educate them a little. I imagine 95% of their business is providing low-flow O2 from concentrators to people with COPD-type ailments. For those people they typically also supply not a mask but nasal cannula. You need a mask.
For relief from CH, you want the purest O2 possible. That also means that when you get your mask, you might find that there is a circle of small open holes in it. Usually, one set of holes has a gasket behind it but one is completely open. Because you do not want to inhale any room air, you should cover the open holes when you inhale. You can use tape, or your thumb. You also want to hold the mask firmly to your face so that you get a tight seal. Eventually, or right away, you should get the mask that's made for people with CH: http://www.clusterheadaches.com/ccp8/index.php?app=ecom&ns=prodshow&ref=clustero2kit