Yes, you do need some additional tests. Your TSH is at a good level, but that does not preclude the possibility of central hypothyroidism. Also, 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. You have mentioned a number of symptoms that are frequently related to being hypothyroid. Your Free T4 is right at the middle of the listed range, which is a good level; however, I don't recall seeing such a narrow range for Free T4. Please confirm that is correct.
You were also tested for Total T3, which is 43% of its range. For the future you really need to make sure they always test for Free T3, not Total T3. Free T3 is the thyroid hormone that is used by all the cells of your body to create all the necessary body functions. So you really need to know your Free T3 level, in order to know if your body is adequately converting T4 to T3. In addition there are many other things that can affect thyroid hormone levels and effects at the cellular level (tissue thyroid effects).
So I suggest that you try to get some additional tests done. Specifically I suggest getting Free T3, Reverse T3, cortisol, Vitamin D and ferritin. You can read about this in the following link. To confirm what I say, I highly recommend reading at least the first two pages, and more if you want to get into the discussion and scientific evidence for all that is recommended. If you want to get an idea of all the processes and variables that can affect tissue thyroid effects, also have a look at Fig. 1 on page 7 of the link.
http://www.thyroiduk.org.uk/tuk/TUK_PDFs/diagnosis_and_treatment_of_hypothyroidism_issue_1.pdf
A good thyroid doctor will treat a hypothyroid patient by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms, without being influenced by resultant TSH levels. Symptom relief should be all important, not just test results, and especially not TSH results. Good thyroid doctors are somewhat hard to find, and may be even more difficult from your description of your location. You cannot just assume that an Endocrinologist is a good thyroid doctor, for a number of reasons. Many of them specialize in diabetes, not thyroid. Many of them have the "Immaculate TSH Belief" and only pay attention to that, which doesn't work for the patient. Also, many of them use "Reference Range Endocrinology" and will say that a thyroid test result that falls anywhere within the range is adequate. That is also wrong. as you can read in item 4, page 5 of the link.
Not sure how you should proceed. You can try to influence your current doctor by giving him a copy of the full paper in the link and asking for the additional tests, and also ask to be treated clinically as described above. If that fails then the Endo would be next I suppose. If so, then you could use the paper and try to get the testing and clinical treatment you need there.
Just in case we might know of a doctor that has been recommended by other thyroid patients in your general area, where are you located and how far are you willing to travel to find a good thyroid doctor?
Sorry you are going through this. I am hoping that a few of the experts on here see your post soon so they can shed some light on this for you. I am an RN but believe me when I say that the info in nursing school and even for mds is limited--that's why they have endocrinologists. My personal experience is from my having hyperthyroidism--for me Graves. I know a few things that might help you but there are some great experts on this site. A few of my favorite experts on here are gimel, goolara, and Barb. They should be able to give you some great info. From looking at your labs I don't see a free t3 which really is important to know. I also know that many times it is important to have vit D level, vit B 12 level, and ferritin levels.
This is a great site--it was my lifeline (emotionally and information-wise) as I went through my ups and downs with my thyroid. My problems started in 2011. You will feel better once they get all straightened out. Hang in there--there is hope.