Yes you can have symptoms generated by your thyroid even when levels are within "normal" range. When I was having symptoms, my levels were within normal range but they were up near a 4 so my doctor wanted to bring me back down toward the 1-2 range to see if it helped. I had recently switched to a new doctor at that point because I was having a hard time convincing my two previous doctors that something wasn't right with my thyroid because my levels kept coming back within normal range.
My symptoms were weight gain-it seemed like 1-2 pounds per week, anxiety and panic, feeling "off", muscle aches especially near and in my joints, muscle twitching and spasms/jerking, sometimes it felt like I had an electric shock feeling in my spine...all these symptoms made me think I had a neurological disorder. I was convinced I had MS.
Since tweaking my medication, I feel about 85% better. For the most part the muscle aching and twitching is gone although sometimes I get muscle jerking in the back of my neck/head region....which worries me still. My weight gain has stopped and I am able to stay at a healthy weight. I don't think my thyroid is completely balanced yet but I definately have improved.
Another thing you can look into is benign fascilation syndrome. Docs don't understand why people develop this condition but it basically consists of muscle weakness, pain and twitching but is seemingly harmless.
I would suggest asking your doc to go over your lab results once more and see where in the range your levels fall. Also, if the doc only tested your TSH levels, it may not be enough information to properly diagnose you especially if you have something like Grave's going on.
Hope this helps.