Definitely get your thyroid under control or this will go on forever as it did for me. An endocrinologist is not necessarily better than a GP, in fact, sometimes worse. There is a thyroid advocate who has a website that gives recommendations from patients who are happy with their docs. Google Mary Shomon - top doc list. From there, keep trying till you find a doc that treats you and your body and not the damn thyroid panels. Also they should check your adrenal function in conjunction with the thyroid. Any doc who does not check both- move on as they don't know what they are doing. Adrenals have to be treated first if there is a problem there or the thyroid meds won't work.
Also due to this weight being on your tummy, I would also suspect a blood sugar problem that is probably being exacerbated by the thyroid or vice versa. Most thyroid patients find that they have to eat low carb all the time and that will solve the blood sugar/insulin problem - usually.
Additionally, none of this will help unless you make exercise a priority, even on the road.