When attempting to diagnose for possible hypothyroidism, the most important indicator is symptoms. An individual symptom is considered non-specific since it can have several causes. Having multiple symptoms that are often related to hypothyroidism, like you have, is strong evidence of hypothyroidism. TSH is useful as a diagnostic only when at extreme levels. Your TSH is high enough currently to also indicate hypothyroidism. Your previous tests for TPO ab and TG ab were positive for Hashi's. Even though your FT4 and FT3 were within range, that does not preclude hypothyroidism. The reason for that being the ranges are far too broad and skewed to the low end due to the erroneous assumptions used to establish the ranges. Your FT4 of .6 is only at 9% of its range , which is too low, and your FT3 is at 39% of its range. Since you were only taking 15 mg of Armour, which contains only about 2 mcg of T3, I expect that the FT3 being higher in range than FT4 is an indication that your body is converting extra T4 to T3 in an attempt to maintain thyroid function as best possible.
So there is strong evidence that you are hypothyroid and in need of thyroid med adequate to raise your FT4 and FT3 levels enough to relieve all those hypo symptoms. I cannot account for why your levels went out of range with the relatively small dose of Armour, unless the Hashi's had affected your thyroid gland enough that it was leaking thyroid hormone faster than normal. So you need to check this out before proceeding with thyroid medication.
So the first thing I suggest is to get an ultrasound test for your thyroid gland to determine the general condition. You also should get a test for cortisol level. The last one you had was for the possibility of Cushings, which was negative. That test would not show if you were normally low in cortisol. In addition, you need to supplement with D3 to get your Vitamin D to above 50 ng/mL. Also you need to test for B12 and ferritin, since hypo patients are so frequently deficient in those. B12 should be in the upper part of its range, and ferritin should be at least 100.
If you want to confirm what I have said, click on my name and then scroll down to my Journal and read at least the one page Overview of a paper on Diagnosis and Treatment of Hypothyroidism: a Patient's Perspective. If you have trouble getting these tests from your doctor, give him a copy of the Overview and maybe that will help persuade him of the need.
Those labs certainly are hyper, but could not be caused solely by taking only 60 mg of Armour, since serum thyroid levels are the sum of both natural thyroid hormone and any thyroid medication. The output of natural thyroid is dependent on the amount of stimulation the thyroid gland gets from TSH. A TSH of .01 would not stimulate any production of natural thyroid hormone, and as I said the 60 mg of Armour is not enough to account for those FT4 and FT3 levels. So I would look for other causes.
Your TPO ab and TG ab indicate Hashimoto's Thyroiditis. With Hashi's people often go through a hyper phase, and then as destruction of the gland continues, they end up hypothyroid. There is also the possibility tht the Hashi's has caused nodules on your thyroid gland that leak hormone faster than normal, which could account for the levels you have. This leads me to ask for your lab results at the time you were diagnosed hypo and started on the 30 mg of Armour.
There is also much more to discuss regarding cortisol, Vitamin D, B12 and ferritin, but let's look first at your test results and reference ranges that resulted in the hypothyroid diagnosis.
When you say you went hyper, what do you mean? Was that based on test results or that you had hyper symptoms? If test results, please post all your thyroid related test results from before and after starting on the med, along with their reference ranges shown on the lab report. If due to symptoms, please describe them for us.