There is lots to discuss, but first please post the reference ranges shown on the lab report for those test results. Also, symptom evaluation is even more important than tests, so please tell us about any symptoms you are having currently.
With those symptoms and your low Free T4, you need to increase your med dosage. The goal is to get Free T4 to mid-range, and thus get Free T3 into the upper part of its range. A suppressed TSH does not mean hyperthyroidism, unless there are accompanying hyper symptoms due to excessive levels of Free T4 and Free T3. In the untreated state our bodies produce a continuous low flow of thyroid hormone. When taking a significant dose of thyroid med in only one or two doses, it suppresses TSH for extended periods.
In addition, hypothyroid patients are frequently deficient in Vitamin D, B12 and ferritin, so those should be tested and then supplemented to optimize. D should be at least 50 ng/mL, B12 in the upper end of its range, and ferritin should be at least 100.
If you want to confirm all this, click on my name and then scroll down to my Journal and read at least the Overview of a paper on Diagnosis and Treatment of Hypothyroidism: A Patient's Perspective.
I wanted to mention also that you should make sure to defer your thyroid med until after the blood draw for thyroid tests, to avoid false high results. Also make sure they always test for both Free T4 and Free T3 every time you go in for tests.