Even though your TSH is suppressed below range, that does not mean you are hyperthyroid unless you have hyper symptoms due to excessive levels of Free T4 and Free T3, which it sounds like you don't have. For confirmation of that, there are scientific studies that show that TSH is frequently suppressed when taking thyroid med. You can read about that in Recommendation no. 10 on page 13 of the following link. I also suggest reading at least the first two pages, and more if you want to get into the discussion and scientific evidence of all that is suggested in the paper.
http://www.thyroiduk.org.uk/tuk/TUK_PDFs/diagnosis_and_treatment_of_hypothyroidism_issue_1.pdf
Before further discussion, please post your actual thyroid test results and reference ranges shown on the lab report. Also, please tell us bout the symptoms you have currently.