Hypothyroidism, need to take thyroid hormone pill. TSH value doesn't matter, main thing is T4 what thyroid gland is producing and its low in your case.
From your post I expect that you are in the UK, so what you are hearing from the doctor would be the typical practice, as prescribed by the NHS. Since your TSH is within the range, they don't intend to treat you. If your TSH was above the range, but less than 10, they also would not want to treat you, if your Free T4 is within range. However, that may not be the correct approach. There is much we ned to discuss, but first please tell us about any symptoms you have. Also, since your TSH levels are not typical of Hashi's, please tell us how that was diagnosed. If it was diagnosed based on antibodies tests, please post the test results and reference ranges shown on the lab report.