My first thought reading the first paragraphs was hemicrania continua (HC). https://my.clevelandclinic.org/health/diseases/21538-hemicrania-continua It's a characteristic of HC, in contrast to CH, that oxygen doesn't work the way it does with CH (which I would say is true of what you are describing). Also, triptans typically don't work, either. But sometimes they work a little.
There are several types of hemicrania. The good news, if you have a hemicrania, is that it is treatable with a medication, indomenthacin. In fact, that is the diagnostic test for hemicrania -- whether indomethacin successfully treats it.
If you do have reason/opportunity to test Indo, be sure to look around the web for proper dosage. There are a lot of recommendations about that.