My first thought was that whoever asked for these tests doesn't know much about treating thyroid. And that it may make sense to possibly consider finding a different Dr.
As stated above TSH is at best a screening tool and that is the only test that really is even remotely relevant. And I personally do not trust TSH as far as I could throw a small adult.
As stated above the most relevant tests are the FREE T4 and the FREE T3.
I mean they aren't if you have symptoms of a thyroid condition.
TSH is really the only valid test that was done.
Thyroxine is Total T4, and is considered obsolete, as it shows the total amount of T4 in your blood; we're concerned with amount of Free T4 in your blood.
T3 Uptake and Free Thyroxine Index are both obsolete ways of calculating Free T4.
The tests you should have done are Free T4 and Free T3; you don't need Total T4 or Total T3 - they are both obsolete.
All of that said, your Total T4 is very low in it's range, so we could probably figure that Free T4 would be equally low. This would indicate hypothyroidism.
With a TSH as low as yours and low T4, we would expect Central hypothyroidism, which is a problem with the pituitary gland, rather than the thyroid gland.
Can you get another set of tests to include Free T4 and Free T3?
Do you have symptoms of a thyroid condition? What symptoms do you have?