Both your FT3 and FT4 are too low in the ranges... most of us feel best with FT4 at about mid range and yours is only at 31% of its range. Likewise, most of feel best with FT3 in the upper half to upper third of its range and yours falls short of that goal also, at only 44% of the range, so it's entirely possible for you to be having hypo symptoms...
Many of us have symptoms long before Hashimoto's has done enough damage to make our actual thyroid hormone levels go below the reference ranges. In addition, many doctors only look at TSH and your is textbook perfect, so she may not even have thought anything about how low in the range your FT3 and FT4 are.
I might suggest a different doctor, if this one is unwilling to change her mind about trying you on a trial dose of thyroid hormones to see if helps alleviate your symptoms.
Oops my free t4 result is 0.94.....thanks for your quick reply Barb135.
Your antibody tests are certainly enough to be the basis for a diagnosis of Hashimoto's, so I'm in total agreement with your doctor, there... as to whether nothing should be done or not, I can't really agree on that.
Many people have symptoms of hypothyroidism, even though their actual thyroid hormone levels are within the so-called "normal" ranges. We all need different levels in order to feel our best.
What's your actual Free T4 result? You listed the reference range, but forgot to put your result.