I'm not sure whether you understand what hypothyroidism is.
You become hypo when your body doesn't make enough of the thyroid hormone. Then, your thyroid sends out a distress signal to the body (called TSH). The TSH is what is measured in your blood work. The less thyroid hormone there is, the more distress signals are sent out. The standard way to treat it is by adding more thyroid hormone (using either T3 or T4 medications, or both).
Like Judy said, it takes a while for the synthetic hormone to build up in your body. You can start to feel somewhat better right away for a myriad of reasons, but the main benefit may not come until 60 days after reaching the appropriate dosage of the medication.
Here's a link for more info on what hypothyroidism is:www.endocrineweb.com/hypo1.html