The meds take about 2 weeks before you will notice much of a change and up to 4-6 weeks to reach their peak of accummulation, at which point they may need to be readjusted until you hit the correct dosage.
What dose are you on? and which medication were your prescribed?
TSH is totally inadequate as a diagnostic for thyroid status. 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 (not the same as Total T3 and T4). When taking thyroid meds, TSH becomes almost useless as the diagnostic by which to determine med dosage.
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.
So, I suggest that you go back and request to be tested for Free T3 and Free T4. If the doctor resists, then you should insist on it and don't take no for an answer. For those tests, be aware that just because results fall somewhere in the reference range does not mean that is adequate for you. Many members here, myself included, say that symptom relief required that Free T3 was adjusted into the upper third of its range and Free T4 adjusted to around the middle of its range. While you are there, you should also request to be tested for Vitamin A, D, B12 and ferritin. Hypo patients often find they are low in those areas as well.
When test results are available, please post results and reference ranges shown on the lab report and members will be glad to help interpret and advise further. While you are at the doctor's you should also ask if he is going to be willing to treat you clinically, as described above. If not, then you will need to find a good thyroid doctor that will do so.