I would still consider the glaucoma check. I don't think that you can even necessarily get a Flammer syndrome diagnosis, it's not a disease afaik, just a pattern.
Glaucoma is the condition that matters and if you don't run the (fast, cheap, painless) check you can miss a serious issue.
I have had mild tinnitus my whole life (with no obvious lifestyle cause), and my migraines do often manifest as pain / pressure behind the eyelid. But I don't have any of the myriad other symptoms listed for Flammer syndrome - I sleep fine, my blood pressure is fine, I'm pretty solidly built (not underweight), I don't get cold easily, etc.
It is interesting to consider I might some sort of related disorder, though!