I would say that parts of it sound like CH (pain in eye/jaw; very tight muscles) but many parts don't sound like CH to me (15 attacks/day, 8-hour attacks, pain brought on by "minor" activities such as turning head, opening mouth, brushing hair). To me, some of it sounds more like TN, and some of it sounds more like paroxysmal hemicrania or hemicrania continua.
Do you have redness or swelling around your eyes? Do your eyes water when you have an attack? Does your nose run or get stuffy? Do you feel like it's almost impossible to stay still during an attack, like you have to keep pacing around or moving in some way?
What medications have you tried? Oxygen? A triptan injection (such as Imitrex) or nasal spray? Steroids? Are you saying none of these consistently help?
Have you been given Indomethacin to try? Gabapentin (Neurontin)? Lithium?
You might consider the Vitamin D3 regimen, which has been shown to help multiple "headache" conditions: https://clusterbusters.org/forums/topic/1308-d3-regimen/