Please also know that in people who are on replacement thyroid hormone it is not unusual for their TSH to be "suppressed", and no longer accurately reflecting their actual thyroid hormone levels.
FT3 and FT4 should always be tested, and their levels (ideally at least mid-range), should take precedence over TSH.
No, unfortunately you ran into one of the many doctors that have the "Immaculate TSH belief" and only pay attention to TSH to diagnose and medicate a hypo patient. That does not work. If those doctors go beyond TSH it is usually only to test for Free T4, and then they use "Reference Range Endocrinology", by which they will try to tell you that a test result that falls anywhere within the so-called "normal" range is adequate. That is also wrong.
TSH is a pituitary hormone that is affected by so many things that at best it is only an indicator to be considered along with more important indicators such as symptoms, and also levels of the biologically active thyroid hormones, Free T3 and Free T4. Scientific studies have shown that Free T3 correlated best with hypo symptoms, while Free T4 and TSH do not correlate. In addition, many doctors don't know that scientific studies have also shown that patients taking thyroid meds frequently find that their TSH becomes suppressed. That doesn't make the patient hyper, unless there are hyper symptoms, due to excessive levels of Free T3 and Free T4.
A good thyroid doctor will treat a hypo patient clinically, by testing and adjusting Free T3 and Free T4 as necessary to relieve symptoms, without being constrained by resultant TSH levels. Symptom relief should be all important, not just test results. You can get some good info from this link written by a good thyroid doctor.
http://www.hormonerestoration.com/Thyroid.html
So you really need to find a good thyroid doctor that will treat you clinically, as described. If you would like help with that, we may be able to provide some doctors that have been recommended by other hypo patients.
Whatever doctor you see in the future, you should insist on always being tested for Free T3 and Free T4 every time you test. Also, since hypo patients are frequently too low in the range for Vitamin D, B12 and ferritin, those should be tested also. Low levels of those cause symptoms, and low D and ferritin affect metabolism of thyroid hormone.