Welcome to our forum,
Don't worry as you have joined a group who have/had symptoms similar to your own and I shall give you a list and I am sure you will find more that fits the bill
It is a learning curve but slow and gradual is fine and you will read, learn and ask questions and you will know more than most doctors.
When you have a blood test for thyroid hormones, it has to be the earliest possible, fasting (you can drink water). If you were taking throid hormones you'd allow a gap of 24 hours between last dose and test and take afterwards.
If your blood test was later ask if you an have a new one. Ask for TSH T4, T3, Free T4, Free T3 and thyroid antibodies. If he is reluctant say you've taken advice from the NHS Choices for information etc on dysfunctions of the thyroid gland and you've ticked all of the sympitoms you have. Show him list. I doubt doctors know any.
When referring to blood tests and doctor says 'normal' that only means they are somewhere in the normal range. He doesn't refer to low or high.
You need to supplement with Vitamin B12 methylcobalamin sublingual as you have to aim for a result above 500 and preferably aim for 1,000. I find Amazon has the best choice of sublingual (dissolve under tongue) as we usually have digestive problems so sublingual is best and methylcobalamin and not cyanocobalamin.
You need to know Vit D, iron, ferritin and folate as we can be deficient which also cause symptoms.
Always get a print-out of your results with the ranges for your own records and post if you have a query.
If your doctor says he cannot do FT4 and FT3, say you have know to your Free T3 as it could be due to low T3 that you have been diagnosed as 'depressed'. If he refuses and if you can afford it we have recommended labs which do home pinprick tests.