For us to give you the best response, we need to know what are the signs and symptoms you mention. Those are even more important than test results. Also, please list the reference ranges for those test results. Test results and their calculated reference ranges can vary from lab to lab, so results have to be compared to ranges from same lab.
The TSH. Range for this lab is .35-3.7 and my level was a 2.59 , the tange for free thyroxine is .76-1.46 my lab value was .86 , range for free triiodothyronine is 2.2-4 and mine was 3.1, TPO antibodies it says range is <60 and mine was <28, anti thyroin globulin antibody range is <60 and mine was <15 , vitamin d range is 30-100 mine was 9 my signs and symptoms are weight gain and trouble losing weight in 5 years since I've graduated high school I have gained 66 lbs and have a hard time losing with multiple workouts , eating better and tracking food, cold extremities, always very tired I take naps all the time then sleep at night and still tired , and depressed mood and "fog brain" at times.
Symptoms are the most important indicator of hypothyroidism. Your symptoms are very indicative of hypothyroidism. Your TSH, TPO ab, and TG ab results do not indicate primary hypothyroidism (Hashimoto's Thyroiditis). Your Free T4 is only at 14% of its range, while your Free T3 is at 50% of its range. Taken together that indicates you are low in Free T4, and your body is trying to maintain thyroid function as best possible by converting more T4 to T3. Note the following info from 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." The ranges are somewhat different but the message is clear.
So your symptoms, and your test results indicate the likelihood of central hypothyroidism. With central hypothyroidism, there 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 hormone. So your next step is to find a doctor that will accept that your symptoms and test results are indicative of hypothyroidism, and agree to treat you. A good thyroid doctor will treat a hypothyroid patient clinically by testing and adjusting Free T4 and free T3 as needed to relieve hypo symptoms, without being influenced by resultant TSH levels. You can read about this in the following link. I recommend reading at least the first two pages, and more if you want to get into the discussion and scientific evidence supporting everything in the paper. You can also use this paper with your doctor to try and get the necessary tests and clinical treatment. If your current doctor resists, then you will need to find a good thyroid doctor that will do so.
Since hypothyroid patients are frequently too low in the ranges for Vitamin D, B12 and ferritin, those need to be tested and supplemented as needed to optimize. D should be at least 50 (your level of 9 is terribly low), B12 should be in the upper end of its range, and ferritin should be at leasts 70.
Please let us know how you progress with the doctor.