Lab tests results don't enable diagnosis as to euthyroid, mildly hypothyroid, or hypothyroid, etc. TSH is a pituitary hormone that is affected by so many things that at best it is only an indicator, to be considered along with more important indicators such as symptoms, and also levels of the biologically active thyroid hormones, Free T4 and Free T3. In the majority of cases, a hypo patient taking adequate thyroid med will find that their TSH becomes suppressed below range. That does not mean hyperthyroidism unless there are hyper symptoms due to excessive levels of Free T4 and Free T3.
Free T4 testing alone does not provide evidence of having adequate conversion of T4 to T3. You should make sure they always test for both Free T4 and Free T3, since Free T3 is the thyroid hormone used by all the cells of the body to produce needed energy, and you cannot be sure of adequate conversion of T4 to T3 without testing of Free T3.
In addition, there are many other things that can affect what is called tissue thyroid effects. Inadequate tissue thyroid effect causes symptoms. For example, in the conversion of T4 to T3, Reverse T3 is also produced. If conditions cause excess RT3 to be produced, instead of T3, is called Reverse T3 dominance, which can result in hypo symptoms. And there are even more variables.
I am giving you all this, not to confuse you but to make you aware that just testing TSH and FT4 is totally inadequate to diagnose or medicate a hypo patient. If you want to confirm what I am saying, read at least the first two pages of the following link, and more if you want to get into the discussion and scientific evidence supporting all the recommendations. I also suggest having a look at Fig. 1 which depicts the thyroid processes and variables affecting tissue thyroid effects. Note that Sugg. 6 on page 2 lists the thyroid tests that should usually be done. For you I suggest that you go back and get tested for Free T3, Reverse T3, cortisol, Vitamin D, B12 and ferritin.
http://www.thyroiduk.org.uk/tuk/TUK_PDFs/diagnosis_and_treatment_of_hypothyroidism_issue_1.pdf
So to answer your question more directly, yes, your symptoms can be caused by hypothyroidism. To enhance that diagnosis and determine the best approach to treatment, you need further testing, as outlined above. In addition, you need a god thyroid doctor. By that I mean one that will treat you clinically, by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms. Symptom relief should be all important, not just test results, and especially not TSH results when already taking thyroid med. So you are going to need to find out if your doctor is willing to treat clinically, as described. Also ask if he is willing to prescribe T3 type meds. If either answer is no, then you will need to find a good thyroid doctor that will do do.