I am hypothyroid and I have no noticeable symptoms except very infrequent periods. So I was screened for PCOS and they did thyroid bloodwork and noticed my TSH was higher than normal. So I did a little research and discovered that the "normal range" varies widely depending on who is defining it (although my TSH, at 6.54, was outside all of the normal ranges I found). I'm not really familiar with the details of hyperthyroidism, but it seems to me that if your bloodwork is borderline, especially if you have symptoms, there might still be a problem. You might consider pushing for more tests or going to another doctor.