When I became severely hypothyroid after having my thyroid killed off with radioactive iodine (thyroid nodules caused out-of-control hyperthyroidism), my Synthroid was not helping all the physical problems I was having; muscle aches, joint pain, extreme fatigue, 22 lbs of weight gain and was beginning to experience night vision problems. Turns out I had developed an intolerance to gluten. In the 18 months before the RAI and subsequent hypothyroidism, I had also had an emergency appendectomy and a mild stroke. Apparently that last health issue with my thyroid, combined with my previous health problems was the trigger. Once I cut all gluten out of my diet, all my problems subsided and was able to once again work out and have lost 22.5 lbs since January. Before I cut out gluten, I could barely make it up a flight of stairs without wondering if I was going to make it up to the top. Until I cut out gluten, every day I felt like a Mack had run over me, I wanted to cry every day. My endocrinologist suggested the possibility of gluten problems. I didn't even consider it a possibility until a gluten-laden weekend at my Aunt's left me feeling worse than I had in my entire life, that's when I looked up gluten intolerance and saw I was suffering just about every physical side effect. Today, I feel better than I have in more than a year.
I agree that the tests often are not accurate in indicating if your thyroid is well managed. It sounds to me like you are experience more symptoms than just the inability to lose weight so I would be persistent in trying to get treated for your symptoms. I would consider another doctor and check our reviews to see if they are patient friendly and be prepared when you see the doctor. Check out this blog post I did. It helped me a lot when I when I was diagnosed. http://thyroiduniversity.com/how-to-prepare-for-a-visit-to-your-thyroid-doctor/
Another thing that I would say is consider a mix of Armour with another medication like synthroid or tirosint (if you have allergies). I didn't feel better and lose weight until I was taking a combination of Armour/Synthroid (which has been switched to Tirosint because I became allergic to Synthroid).