Have I possibly been misdiagnosed?

So, My doctor and endocrinologist tell me I have Graves Disease and HYPERthyroidism. But what I don't understand is all my symptoms point towards HYPOthyroidism. The fatigue, the brain fog, the weight gain...no matter how much I diet and exercise, the confusion and so on and so on. My endocrinologist is being very insistent in giving me radioactive iodine to destroy my thyroid. But if I do that, I will become hypothyroid anyways. I just don't understand and I am getting very upset...mostly over the inevitable weight gain. I mean...I am already fat, I don't need to gain more weight. I've been trying to call her, but she always seems to be out of the office. I've tried all sorts of medications to control the T3 and T4 hormones that are supposedly "out of control" and nothing is working. That's why my doctors want to give me the RAI treatment. I also find it very suspicious that before I went on this medication (methimazole 60mg, recently bumped down to 50mg) I was losing weight left, right, and center...now, no matter how hard I try, I can't lose even an ounce. And every time I go get blood work done to see how the medication is doing me, I am told my thyroid hormones are still "out of control". I am just at the end of my rope here. I just don't understand! Somebody please help me before I make a huge mistake I have to live with for the rest of my life!