Not a doctor, just a hyperthyroid patient. Speaking from experience, yes, you can be hyperthyroid and still have test results "within normal limits".

Took three doctors before I found one who didn't think I was a hyperchondriac. She listened to the symptoms, decided that the "normal" may not be normal for everyone and ordered a nuclear scan. I would have periods of rapid heart beat, but never requiring medical treatment.

Went onto meds and beat the odds--the thyrod straightened itself out without requiring surgery or radiation and I no longer require the meds. Probably, because I was borderline, but I like to think that once in a while we're allowed to win.

Good luck....oh, and yes, you'll probably gain weight if the tone down the thyroid, but you'll feel better.