A normal TSH along with low free T4 and or free T3 can be due to secondary (central) hypothyroidism - this type of hypothyroidism is usually caused by hypothalamic or pituitary destruction (neoplastic, inflammatory, granulomatous, vascular, traumatic, autoimmune, and radiation necrosis). But if you have issues with your pituitary then it's very likely you'll be having issues with other hormones the pituitary regulates as well.
My sister has Hashimoto's thyroiditis (still hasn't started treatment) and last time she was tested her TSH was 0.4 mU/L (0.4 - 4.0) and free T4 was 12 pmol/L (10 - 20). She does not have secondary hypothyroidism. The TSH may have been suppressed perhaps by her illness (she did have Dengue fever at the time) or it could just be due to Hashimoto's thyroiditis (which can cause TSH to fluctuate).
I would recommend testing for two antibodies - thyroid peroxidase antibodies (TPOAb) and thyroglobulin antibodies (TgAb) to see if either one is elevated.
Contrary to what most doctors are taught and their related standard of care, in trying to assess a person's thyroid status, symptoms are the most important consideration followed by levels of the biologically active thyroid hormones, Free T4 and Free T3. TSH is of value mainly to differentiate between primary and central hypothyroidism. Again most doctors only recognize primary hypothyroidism, with a high TSH level due to Hashimoto's Thyroiditis. They also think that central hypothyroidism seldom occurs. I say that is because it is overlooked so often. With central hypothyroidism, there is a dysfunction in the hypothalamus/pituitary system resulting in TSH levels that are too low to adequately stimulate the thyroid gland to produce hormone.
In the words of an excellent thyroid doctor,"The free T3 is not as helpful in untreated persons as the free T4 because in the light of a rather low FT4 the body will convert more T4 to T3 to maintain thyroid effect as well as is possible. So the person with a rather low FT4 and high-in-range FT3 may still be hypothyroid. However, if the FT4 is below 1.3 and the FT3 is also rather low, say below 3.4 (range 2 to 4.4 at LabCorp) then its likely that hypothyroidism is the cause of a person's symptoms." Of course your results are different since they apparently are in different units of measure; however, the message is very clear. Your Free T4 and Free T3 are too low, resulting in symptoms that are frequently related to hypothyroidism. The ranges are far too broad to be functional for everyone, due to the erroneous assumptions used to establish ranges at the lab.
A good thyroid doctor will treat a hypothyroid patient clinically by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms, without being constrained by resultant TSH. Symptom relief should be all important, not just test results.
There is more to discuss, but first please tell us your cortisol result, when the blood was drawn, and the reference range shown on the lab report. Also, please post your Vitamin D and ferritin results.
By the way, I have fatigue, memory issues (maybe because I got obsessed with this problem and cant think about other things properly) and I feel really depressed most of the time. My family says I am pretty aggresive and have been reacting too much to little things. These are relative concepts, so I cannot be sure if I can truely relate these to any kind of thyroid disorder in my case. I just wanted to add this note too in case you'd find them meaningful.