When did testing for thyroid diseases begin? mom had symptoms but the doctors couldn't figure what was wrong.

Almost a century: The old "protein bound iodine" assay dates to the early 1900's. I've seen both hypothyroidism and hyperthyroidism missed for years even when they were obvious. Patients typically got sent to the psychologist or social worker who mistakenly thought they'd been properly screened. Hopefully today's physicians are getting smarter. I trust your mom was finally diagnosed appropriately.