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.