I encourage you to see a thyroid specialist. Internists think they can handle thyroid problems....They can not! What is the doctor doing? Nothing? You have a problem and need a referral to someone who can explain options to you.

It actually sounds like you have T3 and T4 levels and not TSH, which is good, because the T3 and T4 will be the main factors in how you feel. I don't know what your test ranges were, but if they're "slightly high" then you would have hyperthyroidism, not hypothyroidism. Most people with thyroid issues have underactive thyroids, but I think yours is overactive. The heart palpitations are a symptom of an overactive thyroid. Another typical symptom is weight loss, usually not weight gain (although either can be possible). Unfortunately, the weight loss caused by an overactive thyroid means losing a lot of muscle in addition to fat. As someone who had pretty severe hyperthyroidism, I can tell you It's really not the exciting type of weight loss.

My personal, non-medical-professional opinion is that it sounds like you need to be on a thyroid suppressor like methimazole or carbimazole and a beta blocker, at least until your levels return to normal (this is assuming you're not currently on some sort of thyroid replacement meds). I would highly recommend seeing an endocrinologist as soon as possible, and definitely before continuing any sort of diet/exercise regime. Thyroid issues can take a long time to resolve and you're going to need to be patient (at 27 years old, I wasn't allowed to exercise more than going for a walk or change my diet for about a year because we needed everything to get settled first). If you don't take care of this now, you'll only end up doing damage.