Hello from JustAnswer.
There are several comments that are pertinent.
It is unclear why your doctor would change what thyroid tests are being measured. The free thyroid index is an indirect reflection of the free T4 level, but not the T3 or the free T3 level (the thyroid uptake is a measure of protein that carries the thyroid hormone and is used to calculate the free thyroid index). However, since the free T4 level was checked initially, it is unclear why your doctor did not just check the free T4 again. It is true that the TSH is the most important measure of control of hypothyroidism, but if additional tests are to be checked, most doctors would typically check the same labs each time the thyroid tests are done.
The recent TSH of 2.78 is within the normal limit, and achieving a normal level of TSH is the primary goal with thyroid replacement. And in most people, this is all that is needed. There is some evidence that there are a small number of people with hypothyroidism that do better with a TSH that is low in the normal range, about 0.5-1.0. So, in someone on thyroid replacement and a normal TSH that is in the middle or upper portion of the normal range, and is still having symptoms or signs of thyroid disease, it may be appropriate to consider further adjustment of the levothyroxine dose to achieve a level of 0.5-1.0. If your OBGyn thinks that the abnormal bleeding is from other hormonal conditions, then that would support further adjustment of the levothyroxine dose.
There is nothing in these labs that address the possibility of PCOS. The hormone levels that may reflect PCOS would be androgen levels, primarily testosterone levels. An ultrasound also is frequently done for the evaluation of PCOS. However, I would expect that your OBGyn would be better attuned to whether further study needs to be done for this condition.
If I can provide any additional information, please let me know.