Lots of people do it this way -- no prescription required: https://clusterbusters.org/forums/topic/5627-notes-about-welding-o2/
Your PCP is probably wrong . . . For a long time, Medicaid didn't cover O2 for cluster headaches, but now it does, or at least it can. This is a little complicated -- regional Medicare/Medicaid centers are allowed to determine whether or not O2 is covered for CH in their regions. And of course, you'd need a prescription. Welding O2, as discussed in that link, works fine, with no prescription needed.
Since you are new to CH (we don't actually think there is such a thing as "cluster migraines," except maybe for a very, very small percentage of people), you might look at this file: https://clusterbusters.org/forums/topic/6213-basic-non-busting-information/