Most O2 suppliers don't know anything about CH, so they are likely to give you the wrong stuff. If you get a prescription and decide to go forward, call the supplier before they deliver anything. Be sure that they understand that you need at least one large tank (an M tank or an H tank), at least one smaller tank (an E tank) for portability, a regulator that goes up to at least 15 lpm (the prescription will state a flow rate, probably 15, but if you can get the doc to write it for 25, that would be great), and a NON-REBREATHER mask. Let us know how that goes. The mask will work but you could also order a mask specially designed for people with CH, which many people find to be a very big improvement: http://www.clusterheadaches.com/ccp8/
There have been two people here who underwent a lot of hormone replacement therapy because they were transitioning. As I'm remembering, one felt certain that that therapy made the CH worse, and one found the opposite to be true. That's what I think I remember. You could try putting "hormone replacement" into the search bar ) top right of the page) and see what comes up.