I would really encourage looking at a comprehensive thyroid panel, and post the reference ranges. As you noted, the T3 Uptake is archaic, and truthfully it's a waste, it has nothing to do with your T3. Notice how that particular lab came back "low", but the FT4 index is "normal" at 2. To get the FT4 index, you simply calculate the Total T4 with T3 uptake (8.5 x .23 = 1.955, roundup and you have 2). So the two labs are mutually exclusive, yet one is normal and one is low. If you can get Free T4, Free T3, Reverse T3, TPO & TgA, we can provide better comments.
In many physicians eyes, the thyroid is a lot like testosterone. The reference ranges can have a lot of variance, and it's real easy to call it "normal" when in reality it might be far from it. The thyroid can have additional complexities, because you're not only counting on T4 to convert sufficiently to T3, but then you're counting on T3 to get into the body and work at the cellular level. Other variables like iron, cortisol, D3, B12, etc., ALL play a role with this, and running a RT3 lab will help you and your physician know that your FT3 isn't backing up, better known as "pooling".
The guys are giving you some good advise with everything else, so hopefully some or all of this will be beneficial for you. Just let me know if you have any questions with anything I posted above.