I have suspected hyperthyroidism in the past but when I went to see a specialist she asked me how long have I had this weight gain issue and I told her ever since I could remember. She shot down hyperthyroidism and told me that if that were the case I would have gotten a thyroid storm by now. I do have bulging eyes and light sensitivity as well but she said there is no correlation when it comes to me. I didn't get any actual tests ran because she said iy would just be a waste of money for me.
I've always been severely underweight and have always found it impossible to gain and keep on both weight and muscle. I'm saying since I was like 5 I have always been super skinny and I'm just sick of it.
There are other symptoms that can be good indicators of hyperthyroidism including a slightly elevated body temperature and diarrhea. The bulging eyes along with the other symptoms you have already mentioned though really sounds like hyperthyroidism. Sounds like you need to find a different doctor.