Your TSH is indeed indicative of being hypothyroid, what Levothyroxine brand name have they put you on? is it generic or brand name? it is better to be on brand name levo so that your weekly dose remains consistent, with generic your pharmacy might change the supplier and thus changing the formulation of the medication which in turn alters the amount absorbed.
What is your weekly dose of levo? this is very important to start on an amount which is proportional to the initial TSH you have, and then to increase as need based on TSH.
You also need to ask your doctor to test you for the Hashimoto's disease antibodies, those are TGab and antiTPOab if positive then there is no need to repeat the test.
Also two weeks since starting levo is not enough time, the result will be only a noise and not informative at all, you need to be on the same medication and weekly dose for at least six weeks and only then to perform TSH, FREE T3 and FREE T4, but the TSH is the most important and remains the golden standard by which to diagnose and treat thyroid patients.
BTW, Levo can cause side effects if you are over medicated for example, or if your body does not tolerate a certain brand/formulation.
Best of luck and keep us updated,