There is much to discuss, but first a question. What labs did the Endo order for you? Please post the results and reference ranges shown on the lab report.
Since lab results and associated reference ranges vary from lab to lab, in order to assess properly those I also need the reference ranges shown on the lab report.
So your most recent labs before the dose change was Free T4 at 1.57, which is 79% of its range, while Free T3 of 3.0 was at 43% of its range. This is kind of typical for a hypothyroid patient taking T4 med. The Free T3 lags Free T4 because of inadequate conversion of T4 to T3. The correct definition for hypothyroidism is "insufficient T3 effect in tissue throughout the body, due to inadequate supply of, or response to, thyroid hormone". It appears that your Endo is one of the few that is not fixated on just TSH since he responded to your symptoms and lab results in the correct way by slightly reducing your T4 med and adding T3. By the way the conversion factor for T3 to T4 is 3. So the increase of 5 mcg of T3 twice a day is the equivalent of 30 mcg of T4.
So that is all good so far. Next I would point to the part of the correct definition of hypothyroidism involving the "response to" thyroid hormone and ask if you have been tested for Reverse T3, cortisol, Vitamin D, B12 and ferritin. All of these are important since they also have an effect.
In preparation for your next appointment with the doctor I recommend clicking on my name and then scroll down to my Journal and read at least the one page Overview of a full paper on Diagnosis and Treatment of Hypothyroidism: A Patient's Perspective. It will give you all the info you need to make sure the doctor adequately tests you and then treats clinically. Make a copy of the Overview and if the doctor resists then give him a copy and ask him to read and reconsider. Also, keep in mind this conclusion from a recent, excellent scientific study: "Hypothyroid symptom relief was associated with both a T4 dose giving TSH-suppression below the lower reference limit and FT3 elevated further into the upper half of its reference range. "