My unspoken advice was, "under doctor supervision," which I assume everyone understands (I know, a lot people don't.)
You can get a genetic test for FH, but afaik they're rarely performed, although maybe the OP needs one to convince them they really have the condition.
What I suggested was to follow the doctor's advice and, later, under their supervision, adjust statin dosage after lifestyle changes to see if the condition is still present. I'm not a doctor, but I know that my friend's doctor did exactly this - not as a way to convince them they had FH (they were already convinced), but to see if they needed that high of a statin dosage (they did.) That may be what the OP needs to be convinced, while also staying safe.
We both agree that the OP needs to be convinced that they have FH as soon as possible, and should do nothing regarding their treatment without a doctor's approval.