Your NP doesn't understand that symptoms are the most important part of diagnosis, followed by test results. You have a number of symptoms that are frequently related to hypothyroidism. In addition your Free T4 is only at 11% of its range, when it should be at lest 50%. And your Free T3 is actually below range, when it usually needs to be in the upper third of its range. I suspect that your symptoms, FT4, FT3 and TSH results indicate central hypothyroidism, which is a dysfunction in the hypothalamus/pituitary system that results in TSH levels that are too low to adequately stimulate the thyroid gland to produce enough thyroid hormone.
A good thyroid doctor will treat a hypo patient clinically by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms, without being constrained by resultant TSH levels. Symptom relief should be all important, not just test results. You don't necessarily need an Endo, just a good thyroid doctor that will treat clinically, as described.
If you want to try to get your NP to recognize that you are hypothyroid, you may get some usable info from this link and then provide her a copy and ask her to reconsider her diagnosis and see if she will prescribe thyroid med.
http://www.medhelp.org/user_journals/show/2019570/Diagnosing-Treating-Hypothyroidism-A-Patients-Perspective
In view of the probability of central hypothyroidism, I also suggest that you should push to get tested for adrenal function, by testing morning serum cortisol and ACTH. Also, since hypo patients are so frequently low in the ranges for Vitamin D, B12 and ferritin, you should test for those as well and supplement as needed to optimize. D should be about 50 min., B12 in the upper end of its range, and ferritin should be about 70 min.