Have they tested your cortisol? Some of what you are describing are low cortisol symptoms (adrenals)? Particularly being thin with dark circles under your eyes. Being hypothyroid for a long time can cause low cortisol and this is very serious. it will also mean that you cannot cope with the thyroid medication.
Also as others have said, in healthy people, there is a tight correlation between TSH and FT3, but in people who are ill, and on replacement hormones, recent research shows that the relationship between TSH and FT3 is broken and a good doctor will dose someone according to the their FT3 result, you need this in the upper quartile of the reference range.
If you have low iron, low Vit D, low cortisol etc then your body's ability to convert levothyroxine to FT3 will be compromised and you might need a prescription of T3 to add to your T4.
It is possible to get better, it really is, but most of us have found that we need to be advocates for ourselves and that means, unfortunately, learning how this all works so we can educate our doctor - the thing to remember is your doctor works FOR you, and he or she does things FOR you and not TO you. CONSENT is a very big deal in medicine and you need to be able to give informed consent to all that happens to you. I appreciate when you are tired, ill and scared it's difficult to process all this information but it really will help if you can learn as much as you can. Always get copies of your blood results, and buy yourself a big diary and keep track of your dose, your symptoms, your morning temperature, your diet, any supplements, and dose changes and log everything, then if something goes better or worse, you can go back and figure out what happened. I take pulse, BP and temperature everyday, and I weigh myself regularly and write it all down.
In years gone by, before they developed thyroid blood tests, a thyroid condition was diagnosed by cholesterol results, and you may find that without the statins, keeping an eye on your cholesterol levels will give you a good indication of how you are responding to treatment. The problem with statins is a whole other debate in and of itself.
Hang in there, it does get better eventually, and we'll help you along the way.