Yes........you definitely can be hypothryoid with your normal range readings.
I was very easily diagnosed and so was my mother by going to our GP's and getting simple blood workup. That doesn't work for many people.
My sister on the otherhand had worse symptoms then my mother and I combined - she was a wreck. She went to her regular family doctor complaining of a multitude of symptoms for over a year and half. Her blood work always came back showing her thyroid in the normal range. FINALLY, they recommended and endoctrinologist and she went and they found she was hypothyroid also.
She showed in the normal range but is having to take a higher dosage of the same medication I'm on and I was showing a tsh level of 11.93 when first diagnosed.
You need to get to a endoctrinologist. Your thyroid is part of your endoctrinal system. Your insurance may require that your regular doctor recommend a specialist. Ask about doing that.
I read a book called Hypothroidism 101 and the Dr. that wrote it said there are 100,000's of people walking around who are hypothryoid but not aware of it because their blood work is not showing up right.