Before further discussion, please list the reference ranges sown on the lab report for those test results. Also, please note that TSH is a pituitary hormone that stimulates the thyroid gland to produce natural thyroid hormones T4 and T3. Most of that hormone becomes bound to protein and thus is biologically inactive. The small portions of T4 and T3 that are free of protein are called Free T4 and Free T3.
Yours is a very familiar story. For a variety of reasons, many hypothyroid patients are under medicated and continue to have hypothyroid symptoms. The main cause is the belief of most doctors that TSH is an accurate indicator of a patient's thyroid status, in all situations. This belief is totally incorrect. TSH has only a weak correlation with thyroid hormone levels, and has a negligible correlation with hypothyroid symptoms. The only time TSH is an adequate diagnostic is when it is at extreme levels indicative of either overt primary hypothyroidism or hyperthyroidism.
When a hypo patient is prescribed T4 med like Levothyroxine, there are usually two major problems that prevent feeling normal. First is that the doctor will try to adjust medication dosage as needed to keep TSH at a level within the range that satisfies the doctor. Since taking thyroid med spikes levels for several hours, that has a suppressive effect on TSH for most of the day. So trying to determine dosage based on a TSH test almost always ends up with inadequate dosage. Second is that taking thyroid medication affects the conversion of T4 to T3. Since it is Free T3 that largely regulates metabolism throughout the body, you must have adequate Free T3 levels to feel normal. This can be achieved if there is adequate T4 med and it is adequately converted to T3, or from T3 med alone.
Although T3 med alone will work, many people prefer to take both T4 and T3, as needed to get FT4 and FT3 levels adequate to feel normal. FT4 has a longer half-life than T3, which means that levels are more consistent over the day, and day to day. With T3, levels will fluctuate more over the day because of its short half-life. Although there is no evidence of this being a problem, most doctors are opposed to it. I am not sure why the doctor switched you from T4, and then NP Thyroid, to T3 only, instead of a combination of T4 and T3. Seems like that should have been the first trial, so before starting the second T3 tablet of 25 mcg, I suggest you ask the doctor why T3 only, and if you maybe need to add some T4. I don't think your first two doctors did you any favors with their prescribed treatments, but I have hope for the current doctor since he is willing to prescribe T3, which most doctors will not, unfortunately.
If you want to learn more about all this I recommend reading a paper I co-authored, shown in the link.
Arrrrggghhhh!. So frustrating. I wrote a long reply to your post and it did not post. I am going to post this and maybe the other will show up.