When doctors adjust our medication to 'fit' within the TSH level it can cause us more problems. Read the first two questions in this link:
The above two links have good information.
It's your health - not your doctors and we do rely on them normally but, as regards the treatment of hypothyroidism I do wonder. I was worse on levo and it's taken me about 5/6 years to find my way through the maze and am now well on T3 only. Not many doctors will prescribe.
Start from the beginning with your GP. Say you are determined to get better but you do need some blood tests so that you can follow your own method of treatment. Ask for TSH, T4, T3, Free T4 and Free T3, antibodies (if you've not had them before). Vit B12, Vit D, iron, ferritin and folate.
Don't take levo on the morning of the test which should be as early as possible. Take levo after. Fast too. Get a print-out of your blood test results with the ranges (these are important as labs differ). Post results on a new question for members to comment upon them.
Tell your GP it's o.k. to have a suppressed TSH. email email@example.com and ask for a copy of Dr Toft's Pulse Online article. In question 6 you will see that he says that some of us do need a suppressed TSH (ignore his final para which we well know is what many of them think). Dr Toft was President of the BTA so she cannot argue with him although some doctors still stick to the guidelines by keeping TSH 'in range'.