There are antibody tests to determine Hashimoto's thyroiditis and Graves Disease For Hash's TPO and Tgab For Graves TPI
Best Regards FTB4
These tests determine if a thyroid issue is caused an autoimmune disease, Hashi's is Hypoactive/underactive, when the body's immune system does not recognize the thyroid and attacks it, slowly destroying the thyroids ability to produce the T4 hormone. Graves is Hyperactive/overactive, where the immune systems attack causes overproduction of the T4 hormone. Regards FTB4
When referring to T3 and T4, always specify FREE T3 and FREE T4, as they are different from the tests for Total T3 and Total T4. If you don't specify, you will get Total T3 and Total T4, which are considered obsolete and of little value.
Definitive test for Graves is TSI.
While Hashimoto's is most often associated with being hypo, it can also be characterized by periods of of hyperthyroidism, and "swinging" from hyper to hypo.