Gimel is giving great advice.
It is great that you are following up and treating your thyroid levels and I recommend you continue to do so and also get those other vitamin levels checked.
I think however that it is very important that you do NOT forget about your Low Testosterone level. That too can have a dramatic affect on your weight issues as well as energy levels (fatigue and stamina) and muscle tone etc.
I do not know what your age is. But unless you are like an 85 year old man, your Testosterone levels are probably lower than an 85 year old man.
I'm not exactly sure how Testosterone may or may not affect thyroid or the metabolism of thyroid. But it has a huge factor on a man's overall health.
I think there is another forum under sexual health that has or is a place to discuss testosterone hormone issues. So you may also want to check that out!
I highly recommend testing for Vitamin D, B12, and ferritin and then supplementing as needed to optimize. D should be at least 50, B12 in the very upper end of its range, and ferritin should be at least 70. All three are very important, and frequently deficient in hypothyroid patients.
I also would not recommend taking such a big increase in T3 all at once. It could cause you to have a hyper reaction. I would recommend that you add T4 to your med dosage, and get your Free T4 to at least mid-range. Along with that Free T3 should be in the upper third of the range, and adjusted gradually, as needed to relieve hypo symptoms. Body temperature is affected by a number of things other than thyroid, so it is NOT a good idea to dose yourself by temperature alone.
If you want some insight on this subject, please read the first two pages of the following link, and also read further if you want to get into the discussion and scientific evidence for all that is suggested on page 2. Note that recommended tests include cortisol also. Cortisol levels have a big effect on body temperature.
http://www.thyroiduk.org.uk/tuk/TUK_PDFs/diagnosis_and_treatment_of_hypothyroidism_issue_1.pdf
I really suggest that you find a good thyroid doctor that will treat clinically by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms, without being influenced by resultant TSH levels. Symptom relief should be all important, not just test results.
Glad that you are doing much better. From your latest test results the T3 med has suppressed your TSH, and with little TSH stimulation of your thyroid gland, your body is producing very little thyroid hormone. From that your Free T4 is below range, which is not advisable. You need to add a source of T4 to your meds and get your Free T4 to at least the middle of the range.
Have you tested for Vitamin D, B12 and ferritin?
When did you start on T3 med? What is your daily dosage?
I don't understand about the link. I tried it several times and it worked fine. Maybe try this link and then look for the article on the right hand side, in a small box by itself. Diagnosis and Treatment of Hypothyroidism.
http://www.thyroiduk.org.uk/tuk/
Those symptoms are frequently related to being hypothyroid. So that is further evidence of hypothyroidism. In diagnosing hypothyroidism, symptoms are the most important indicator, followed by Free T4 and Free T3 levels.
If you want to do some reading on hypothyroidism, following is a link. I highly recommend reading at least the first two pages and further if you want to delve into the discussion and scientific evidence supporting all the recommendations. You can also note on page 7 the main factors affecting conversion of T4 to T3. Note that carbs are not included as a factor.
http://www.thyroiduk.org.uk/tuk/TUK_PDFs/diagnosis_and_treatment_of_hypothyroidism_issue_1.pdf
I think you need to do some further tests. Specifically, you need to follow up on the increased TSH by testing for the antibodies of Hashimoto's Thyroiditis. Specifically those are Thyroid Peroxidase antibodies and Thyroglobulin antibodies. Tests are shown as TPO ab and TG ab. In addition, it would be good to test for Vitamin D, B12, ferritin, selenium, zinc, and cortisol. You will find most of these listed in Suggestion 6 on page 2.
After those tests I think it will be clearer as to what should be done for treatment. You will at least need a good thyroid doctor that will treat clinically, by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms, without being constrained by resultant TSH levels. Symptom relief should be all important, not just test results.
In case you whould have trouble finding such a doctor, if you will tell us your location, perhaps we know of a doctor in your area that has been recommended by other thyroid patients.
It appears that you have a number of issues that are related to being hypothyroid. Your hypothyroidism is due to your low Free T3 level. Due to the erroneous procedure for establishing ranges, Free T3 and Free T4 in the lower half of the range, is cause for suspicion of hypothyroidism. Your Free T4 is slightly below recommended level, and your Free T3 is actually below the range. I don't remember ever seeing someone with such a low Free T3 when Free T4 is near the middle of the range, so it appears there is a conversion problem.
There is more to discuss, but before going further, please tell us about any symptoms you have.