Sorry, I just noticed that you were in the UK. That presents a whole different set of roadblocks to getting adequately tested and treated for hypothyroidism.
Due to the rules of the National Health Service, doctors try to only test and use TSH to diagnose and treat a hypo patient. That simply doesn't work. If the doctor tests beyond TSH, for Free T4, then they will try to tell you that a test result that falls anywhere within the range is adequate. That also is wrong.
A good thyroid doctor will treat a hypo patient clinically by testing and adjusting Free T3 and Free T4 as necessary to relieve symptoms, without being constrained by resultant TSH levels. You can get some good insight into clinical treatment from this letter written by a good thyroid doctor for patients that he sometimes consults with after initial tests and evaluation. The letter is then sent to the participating doctor of the patient to help guide treatment. In the letter, please note the statement, "the ultimate
criterion for dose adjustment must always be the clinical response of the patient."
http://hormonerestoration.com/files/ThyroidPMD.pdf
So, in order to try and get clinical treatment as described, you have tow alternatives. The first is to follow the advice of a fellow UK member who was successful in finally getting adequate testing and treatment. Here is what she told us.
"What I have learned from my experience is that you have to go to the Dr's office and TELL THEM WHAT YOU WANT and to go backed up with knowledge. You have to tell them that you have done your reading and looked into your condition and care about the long-term treatment of your health and thyroid. If you fight for what you want, you will eventually find someone that is happy to go along with your wishes. But we all have to take charge of our own health, right?"
If you decide to try the first approach, you can get more than enough info to use with the doctor from my posts to l_ftz, on this same page. If you try and don't succeed, or you can go private, then that is alternative two. If you decide to go private, if you will tell us your location, I have names of several UK doctors that just might be close enough to consider.
When already taking a significant dose of thyroid meds, TSH is almost useless as a diagnostic by which to determine dosage. I say that because TSH is a pituitary hormone that is affected by so many things that at best it is only an indicator, to be considered along with more important indicators such as symptoms, and also levels of the biologically active thyroid hormones, Free T3 and Free T4.
Your Free T4 is not too bad, although it could be tweaked a bit, up to around the middle of the range. Your long list of symptoms does not seem to be consistent with that Free T3 result, which also is not too bad, if it is accurate. In view of your symptoms, and the fact that frequently hypo patients taking T4 meds find that their body does not adequately convert the T4 to T3, I suggest that you should request your doctor to test for both Free T3 and Free T4. Also, since hypo patients are frequently too low in the ranges for Vitamin D and B12, I also suggest you request those as well.
Since your ferritin is terribly low, you should consider supplementing with an iron supplement such as ferrous fumarate, or ferrous glycinate. You'll probable need about 75 mg (starting at 25 mg) of either to bring up your ferritin to levels recommended for women (70-80). Low ferritin causes lots of symptoms and also adversely affects proper metabolism of thyroid hormone. So, I also suggest that you should request to be tested for Reverse T3. Reverse T3 is the mirror image molecule of T3. T4 is converted to Reverse T3 along with T3. Under adverse conditions, including low ferritin, excessive amounts of Reverse T3 can be produced, which counteract the effect of Free T3 on tissue, resulting in hypo symptoms. It should be checked out.