Do you have any type of symptoms at all? weakness, fatigue, hairloss, weight gain/loss, jittery, shaky, brain fog, memory loss, excessive hunger, gastointestinal symptoms, muscle pain or weakness, cold or heat intolerance, nausea in the morning? There are many more, so you may have some symptoms without realizing they are related to the thyroid and docs will only tell you the most popular symptoms.
If you have no symptoms you may be one who feels better on a high TSH, although yours is out of normal range where most people feel bad. Better thyroid tests are the T4 free and T3 free, those tell the amount of active thyroid hormone that is in your blood, you may want to have those checked before starting a lifetime of meds.