Starting with your thyroid tests, TSH is a meaningless test when taking significant doses of thyroid med. TSH is suppressed for a majority of people taking adequate thyroid med. The main reason being that the body evolved with a continuous low flow of thyroid hormone. So a large dose taken essentially once daily tends to suppress the TSH for an extended period. So don't let your doctor pay attention to TSH, and erroneously decide that you have become hyperthyroid if your TSH becomes suppressed.
Your Free T4 is a bit lower than we recommend, which is mid-range. So your increase to 200 mcg should take care of that. Your Free T3 is less than 3% of its range, which is terribly low. That is the main cause for your many hypo symptoms. The range is far too broad to the low end, which is explained in the paper I linked above. Free T3 typically needs to be in the upper half of its range, and then adjusted from there as needed to relieve symptoms. As an excellent thyroid doctor told me once, "dosage is irrelevant. Only the physiological effect matters." Since you were taking 10 mcg of T3 at the time of the tests, you obviously need a substantial increase. So you should talk with your doctor about that.
Your ferritin is right at the minimum recommended level, so an increase there to bring it up to 90 should help. I am not too aware of the optimal level for folate, but your level is obviously too low. Same for B12. It needs to be in the very upper end of its range for best effect. Same for Vitamin D. So if those tests are representative of your doses you mentioned then increases would be advisable.
Since your cortisol was done 3 years ago, it would be good to test again because your level was below mid-range. For cortisol the best is a diurnal saliva cortisol panel of 4 tests taken at at different times during the day. This panel tests for free cortisol and is more revealing. Most doctors won't order this panel and will only order morning serum cortisol (total cortisol). If you don't use iodized salt I would do a test for iodine also.
And the next time your thyroid levels are tested, make sure they test for Reverse T3, along with the Free T3 and Free T4.
Sounds like my own story except that I was not even being tested for Free T3. After 20 years or so of being inadequately medicated, while taking 200 mcg of T4, I found this site and learned of the importance of having adequate Free T3 levels. I got mine tested and found it to be in the very low end of its range, even though Free T4 was near the top of its range. My body was not adequately converting the T4 to T3. So my doctor at that time agreed to switch me to Armour Thyroid, to provide a source of T3. After some tweaking of dosage, I felt better than I could even remember.
So at least you are being tested for Free T3 and have been given a T3 med. Now, you being on 200 mcg of T4, which should get your Free T4 above mid-range, it is a matter of also increasing your T3 med to raise your Free T3 level into the upper half of the range, and adjusted from there as needed to relieve symptoms. Symptom relief should be all important, not just test results.
In addition, hypothyroid patients are frequently deficient in Vitamin D, B12 and ferriitin. If not tested for those, you should do so 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 lest 70, and some sources say 100. Optimizing those will help with some of your symptoms. Also, I suggest that you should test for Reverse T3 at least once to establish its level, and also test your morning serum cortisol.
You can read all about this in the following link. I recommend reading at lest the first two pages, and more if you want to get into the discussion and scientific evidence for all that is recommended in the paper.
http://www.thyroiduk.org.uk/tuk/TUK_PDFs/diagnosis_and_treatment_of_hypothyroidism_issue_1.pdf