Doctors don't understand that a person's thyroid status is a result of T3 effect in tissue throughout the body due to both the supply of, and response to, thyroid hormone. Except at extreme levels TSH has only a negligible correlation with TISSUE TE EFFECT, and thus is inadequate as an indicator of thyroid status. Free T4 and Free T3 have only a weak correlation with TISSUE T3 EFFECT, and are useful mainly to support clinical evaluation for symptoms that occur more frequently with thyroid issues than otherwise. Since there is no direct measure of TISSUE T3 EFFECT, and associated thyroid status, an integrated approach is best, including a full medical history and a clinical evaluation for symptoms, supported by expanded biochemical testing.
I am sure your doctor's diagnosis and proposal for prescribed antithyroid med was primarily based on concern for hyperthyroidism, due to the TSH result, combined with high levels of Free T4 and Free T3. Your lack of any identified symptoms was obviously ignored in this diagnosis. It seems to me that more tests should have been done to identify the possible cause for those test results. To assess the possibility of Graves' causing hyperthyroidism, a test for Thyroid Stimulating Immunoglobulin (TSI) could have been done. To find out if the problem was due to nodules on your thyroid gland causing leakage of thyroid hormone faster than normal, since TPO ab was negative a test for Thyroglobulin antibodies should have been done to check for Hashimoto's Thyroiditis.
Especially in view of having no symptoms, and also your personal situation, I certainly would not want to immediately go on antithyroid med at a dose like that, which as mentioned might quickly cause you to become hypothyroid, with all the unwanted symptoms. I would take a more cautious approach and get the additional tests done and then consider options. If you can get those tests done and you would like our opinion of results, please post them here, along with reference ranges shown on the lab report.
There are also several types of thyroiditis which may start with a hyper phase, and then go to a hypo phase. Have you had any discomfort or irritation in the thyroid gland area?