If you have fibromyalgia you need T3 to be added to T4 or maybe some T3 added to your dose. If the doctor says you are depressed - he should have tested your Free T4 and Free T3. If we have low FT3 we need to have some T3 added.
T4 - levothyroxine is inactive. It has to convert to T3. Some of us cannot convert efficiently which means our receptor cells lack T3 which is the only active hormone which runs our whole metabolism.
You need a Free T4 and Free T3 blood test. If GP wont do so, you can have them privately from one of our recommended labs.
I am not medically qualified but know the difficulties if levothyroxine doesn't work as doctors assume.
We have to read/learn and know more than GPs which doesn' take too long.
When you have a blood test for thyroid hormones it has to be the very earliest, fasting, (you can drink water) and allow a gap of 24hours between your last dose of levo and the test and take afterwards. This gives a better result for the patient.