Your original symptoms are frequently related to hypothyroidism, but you did not post any test results from that time. From your most recent test results your Free T4 is typically too low in the range. I won't go into all the details of why, but it should be at least mid-range. TSH is basically a useless test when already taking thyroid med. You were not tested for the most relevant thyroid hormone, which is Free T3. Free T3 is metabolized by cells throughout the body and provides the energy we need. Many hypo patients taking T4 meds find that their body does not adequately convert the T4 to T3, resulting in inadequate levels of Free T3 and associated symptoms. So you need to make sure they test for both Free T4 and Free T3 every time you go in for tests. If they resist, you should insist and not take no for an answer.
Since hypo patients are so frequently deficient in Vitamin D, B12 and ferritin, you should also test for those and then supplement as needed to optimize. D should be at least 50, B12 in the upper part of its range, and ferritin at least 70. All three are important.
In addition, with the reactions you report with the thyroid med, it makes me wonder if you have a cortisol problem. Cortisol is one of the tests that should be done during initial diagnosis. A cortisol deficiency can sometimes cause reactions symptoms like you mention. It is also recommended that any cortisol deficiency should be qddressed before starting on thyroid med.
The best way to test for cortisol is a diurnal saliva cortisol panel of 4 tests from samples taken at different times of day. Doctors don't like to order that test panel and will usually only order a morning serum cortisol test, which is total cortisol and not as definitive as the saliva test which is free cortisol. If you cannot get a doctor to order the saliva tests, you could order a test kit on line and it costs about $140. At any rate I think your symptoms require cortisol testing. Note these symptoms of being low in cortisol
Mental and psychological ailments such as depression
Faintness and dizziness
Weakness and fatigue
Heart palpitations
Emotional hypersensitivity
Inability to cope with stress
Social anxiety
Muscle weakness
Headache, scalp ache, or general body ache
Severe or dull lower back pain
Extremely sensitive skin
Nausea, diarrhea, and vomiting
Abdominal pain and hunger pain despite an empty stomach
Extreme craving for salty foods
Anxiety and jitters
Clumsiness and confusion
Motion sickness
Insomnia and dark circles under the eyes
Low bladder capacity and symptoms of IBS
Irregular or non-existent menstrual peri
Please tell us about all symptoms you have, if there are others. Also we need to know your thyroid related test results and their reference ranges shown on the lab report.