Have you had your thyroid antibodies tested? TSH can be normal and you can still have a problem. High levels of T3 uptake, from my reading, may signal hyperthyroidism. Did you have your thyroid antibodies tested as well? Those can be helpful in diagnosing either Hashimotos or Graves disease.
Total T3, Total T4 and T3 Uptake and Free T4 Index are considered to be obsolete...
Your FT4 is at 40% of its range, which is a bit shy of the recommended 50% of range and your FT3 is at 47% of range, which is also shy of the recommended upper half to upper third of its range. Based on those levels, you could be hypo; however, your TSH is "pristine", so it's unlikely a doctor will consider you hypo... That said, central hypothyroidism is a likely possibility, since it appears that your pituitary gland is not producing enough TSH to stimulate your thyroid adequately.
As kdblack mentioned, you should ask for thyroid antibody tests to rule out Hashimoto's Thyroiditis. Hashimoto's is an autoimmune condition in which the body sees the thyroid as foreign and produces antibodies to destroy it.
The body produces, mostly T4 and a little bit of T3, of the Total T4 produced, most of it is bound by protein and is unusable, so we test for Free T4, to find out how much is free (unbound) and available for use. Free T4 isn't used directly; it must be converted to T3 prior to use.
Like T4, most of the Total T3 in the body is bound by protein and can't be used, so we test the Free T3 to find out how much is free (unbound and available for use. Free T3 is the hormone that's used by every cell in your body.
In your case, your thyroid appears to be making very little of either T4 or T3 (as evidenced by the Total T4 and Total T3), so it appears that most of what you have is Free/unbound.
If you had Hashimoto's, you would actually have a thyroid problem, meaning your thyroid was malfunctioning and we'd expect your TSH to be higher than it is, because your pituitary would be trying to stimulate your thyroid to produce more hormones. As it is, both your thyroid hormone levels and your TSH are low, indicating that it's a pituitary issue and your pituitary is not stimulating your thyroid.
Hypothyroidism is hypothyroidism and must treated with replacement thyroid hormones, just like any other type of hypothyroidism.
The problem is that many doctors will take one look at the TSH, which is well within the reference range and would be considered "pristine" and will say there's nothing wrong, when there obviously is... That's why you have to advocate for yourself.
Because Central hypothyroidism is a pituitary condition, you should also have your doctor check your other endocrine systems to make sure they are all functioning properly... this includes adrenals, reproductive system, pancreas, etc.
If you do not fight for yourself, no one else will, And the Dr's who look only at TSH and or order and use outdated tests will most likely keep you feeling ill.
The conundrum of normal TSH and or FT4 and FT3 both in the "normal" range and you still feel like junk is one of the most common and unfortunate reasons people end up finding this forum. Because they KNOW they feel like crap and the Dr's keep telling them that they are "normal".
The truth is that for most people to feel well the rule of thumb Barb135 states is to be no less than in the MIDDLE of the range. Being anything less than the Middle of the range AND symptomatic is reason to treat with hormone replacement medication. Otherwise you will just be left in limbo and feeling terrible.
Read a lot here and other places and educate yourself and have the courage to stand up and advocate for yourself. This also MAY result in you finding or even going through several Dr's until you find one who is open to listening to you and is truly knowledgable with Thyroid issues. This unfortunately is much harder to find than you would think.