Reverse T3 is the "emergency brake". If you are ill, the body will decrease metabolism and conserve energy. This is called euthyroid sick syndrome - labwork shows low free T3, high reverse T3, normal TSH and normal T4. Your reverse T3 may not be over the range but it's too high at the top cut off range. SIBO is a listed cause of elevated reverse T3.
Wow, you sure do have lots of symptoms that are frequently related to being hypothyroid. In addition, your TPO ab result is consistent with Hashimoto's Thyroiditis, although your TSH level is atypical of Hashi's, so there may be something else that is keeping your TSH low even with the low levels of Free T4 and Free T3. TSH, however, is useful as an indicator only at extreme values. Symptoms are the most important indicator, followed by levels of thyroid hormone.
From the first test results, even though your Free T4 and Free T3 were in the range, that does not mean they were adequate for you. The ranges are far too broad, due to the erroneous assumptions used to establish those ranges. I have no explanation for the significant change in your second Free T3 test but obviously it is even worse than the first test. In addition your Reverse T3 is right at the high limit of its range. Combining that with your low Free T3, the ratio of Free T3 to Reverse T3 is only .64. Recommended levels are 1.8, or in some sources, 2.0. So you can see just how low your ratio is.
I hope that your doctor is not one that only pays attention to TSH. If there is any hesitation about starting you on thyroid med, click on my name and then scroll down to my journal and use the one page overview, and the link included, to try and get your doctor to treat clinically, by adjusting your Free T4 and Free T3 levels as needed to relieve hypo symptoms, without being influenced by resultant TSH levels. Most of us have found that we needed Free T4 at least mid-range, and Free T3 in the upper part of its range, and adjusted from there as needed to relieve symptoms. In view of your low Free T3 in the last test, I would ask the doctor for a desiccated type of thyroid med containing both T4 and T3, like NatureThroid or Armout Thyroid.
Also, hypo patients are frequently deficient in Vitamin D, B12 and ferritin. So you need to get those tested and then supplement as needed to optimize. D should be at least 50, B12 in the upper end of its range, and ferritin should be at least 100. All three are very important to a hypothyroid patient. Low D and ferritin are also factors in excess conversion of T4 to Reverse T3. You can read about Reverse T3 in the link, Recommendation 11 on page 12.
There is much to discuss, but first please tell us about symptoms that you have.