Just because test results fall in the so-called "normal" range does not mean they are adequate for you. Due to the erroneous assumptions used in establishing the ranges, they are far too broad to be functional for everyone. If ranges were calculated based on testing of healthy adults with no known thyroid pathology, the ranges would be more like the upper half of current ranges. For that reason members say that relief from hypothyroid symptoms required Free T3 in the upper part of its range, and Free T4 around the middle of its range, at minimum.
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, and especially not TSH. You can get some good insight from this link written by a good thyroid doctor.
http://www.hormonerestoration.com/Thyroid.html
So if you haven't been tested for Free T3 and Free T4, that should be a priority. Also, since hypo patients are frequently too low in the ranges for Vitamin D, B12 and ferriitn, those need to be checked as well. If you can get all those done and then post results and reference ranges we will be happy to help interpret and comment further. I think that the our very experienced and knowledgeable members can be of significant help to you, so please keep in touch.
Please post your thyroid labs with reference ranges.
If you only started levo last week, I'm surprised that you are feeling better already. It takes levo 4-6 weeks to reach its potential in your blood.
How much are you taking?