I went around the sinus thing, TMJ diagnosis and so on before arriving with the cluster diagnosis. As for teeth, the only pains I have had in my life to register on my cluster scale were an ear infection I had once where Demerol was pumped into me in hospital, kidney stones and when a molar broke and got infected/abscessed, the trigeminal nerve services the top jaw and teeth as well as in around the ear, so I assume that is why the pain was so intense.
You could still be having ch as well as the teeth issues. But abscesses in teeth and jaw can be extremely painful.