All the tests fall in normal ranges.
The TSH is high.
The T3 and T4 are a little low.
But within normal test ranges.
It's classic. Your T3 and T4 will not go out of range until your TSH goes much higher. Your TSH should be somewhere closer to 1.0 or 2.0, and it is high enough to make you feel ill.
Most people have a TSH of between 0.6 and 2.8, with the majority clustering around 1.0 to 1.5.
Your TSH only has to be off by 1.0 on the "normal" scale, before it affects your body. So if you are two or three points too high, you are sick.
You probably won't get treatment until your TSH goes above the lab limit of 5.6, because doctors don't want to put you on meds too soon. But you would feel better if you were on meds now.
You should ask to be tested for thyroid antibodies. Those tests may help a doctor decide when to treat.
TPOab and TGab tests.
LABS
TSH 3RD GENERATION 4.6 NORMAL RANGE 0.34 TO 5.6
T3 UPTAKE 37.4 NORMAL RANGE 32 TO 48.40
THYROXINE T4 8.06 NORMAL RANGE 6.09 TO 12.23
FREE THYROID INDEX (T 7) 7.54 NORMAL RANGE 5.93 TO 13.13
Do you have the lab results handy so that you could post what the normal lab ranges are for each test?
The symptoms all point to hypothyroidism, but I am not familiar with the types of T3 and T4 tests you have listed.
Your TSH is high enough to give you symptoms. You may have "sub-clinical Hypothyroidism", which means you have the symptoms, but may or may not get medication yet.
What did the doctor say?