Maybe give your doctor this link to read particularly this excerpt:
Physicians have various view points as to whether sub-clinical hypothyroidism should be treated. There is no real right or wrong answer, and a lot depends on the patient's preference. One criterion that does help to make a decision as to whether treatment should be started is the cholesterol profile. Patients with a high cholesterol level (particularly LDL, or bad cholesterol) usually benefit from thyroid hormone replacement therapy, since their cholesterol profiles often improve with replacement.
As a patient, if you are diagnosed with "sub-clinical hypothyroidism," you should discuss the pros and cons of starting thyroid replacement therapy with your doctor. Likewise, you should have a fasting cholesterol profile to allow you and your doctor to make an informed decision. Whatever you choose, it is important to remember that you need to have continued follow-ups with your doctor. If you have chosen to start replacement therapy, you will need to check your thyroid hormone levels while on replacement. If you have decided to wait, you will need to have blood tests to follow your thyroid function. Remember that your preference plays a large role in any therapy you choose, so don't be afraid to address your questions or concerns.
This excellent doctor (a Virologist) was hounded by the GMC (not his patients who travelled throughout Britain to see him) because around ten years after the blood tests and levothyroxine was introduced he was being sent patients who had 'mysterious' symptoms and who were diagnosed with cfs/m.e. (new diseases) Because he had been trained as a medical student on all of the symptoms of hypothyroidism he (as all the other doctors around the same age) treated patients with a trial of thyroid hormones and they recovered. He tried to get every Endocrinologist to a meeting to discuss the 'parlous situation of patients' but not one accepted his invitation. They must have been 'frightened off'. On one occasion a patient was told by an Endocrinologist 'we've got him now' just before his next meeting with the GMC. Why, he diagnosed according to clinical symptoms and prescribed.
Endocrinologists and doctors are told to only diagnose according to the TSH which leaves thousands suffering or diagnosed with another illness and prescribed when in reality it may be the lack of thyroid hormones which is causing the symptoms.
If you've not had a recent blood test for your thyroid gland hormones, ask for T4, Free T4, Free T3,T3 and antibodies to be tested and also for Vitamin B12, Vit D, iron, ferritin and folate as we are usually deficient. Get the test as early as possible (TSH is highest then) and fast too. Get a print-out of the results with the ranges and post on a new question for comments. (some labs may not do all of them).
I would say your symptoms are hypo and the fact that you have ME/CFS would be a step in the right direction.