You don't necessarily need an Endo. Many of them specialize in diabetes, not thyroid. Many of them have the "Immaculate TSH Belief" and only pay attention to TSH. That is very wrong. If they go beyond TSH and test Free T4 and find it within range, they frequently will tell you that means all is okay. Wrong again. You just need a good thyroid doctor that will treat clinically, as described.
I am sending you a PM with info on a doctor for you to consider. To access, just click on your name and then from your personal page click on messages.
Your doctor is not taking very good care of you. You have all those symptoms of being hypothyroid and you are still on the same starting dose of thyroid med. Not only were you not yet prescribed a med dosage adequate to relieve your symptoms, Hashi's continually diminishes the output of natural thyroid hormone, requiring increasing med doses until you end up on a full daily replacement amount. A good thyroid doctor will treat a hypothyroid patient clinically by testing and adjusting Free T4 and Free T3 levels as needed to relieve symptoms, without being influenced by resulting TSH levels. Symptom relief should be all important, not just test results compared to flawed reference ranges.
So you need an increase in your thyroid med adequate to raise your Free T4 to at least mid-range, and your Free T3 high enough to relieve symptoms. In the future you should always make sure they are testing you for both Free T4 and Free T3 every time. If your Free T3 level is lower in its range than Free T4 in its range, then that is an indication of inadequate conversion of T4 to T3, which might require the addition of T3 to your med. That can be either be T3 or a desiccated type like Armour Thyroid or NatureThroid, which contains both T4 and T3. The objective is to get your Free T3 level high enough to relieve symptoms.
And you do need to test for Vitamin D, B12 and ferritin, and then supplement as needed to optimize. D should be at least 50, B12 in the upper end of its range, and ferritin should be at least 70. Note that ferritin also is an important factor in your body's conversion of T4 to T3.
If you want to confirm any of this please read at least the first two pages of the following link, and more if you want to go through the discussion and the scientific evidence supporting all that is suggested in the paper.
http://www.thyroiduk.org.uk/tuk/TUK_PDFs/diagnosis_and_treatment_of_hypothyroidism_issue_1.pdf
Do you think your doctor will be receptive to the suggestions to test further and increase your med, including T3 if needed? If not, you can try giving the doctor a link to the paper, or a copy, and ask him to read and reconsider. If all that is unsuccessful getting you treated clinically as described, then you will need to find a good thyroid doctor that will do so.
You have a number of symptoms that can be related to hypothyroidism. Symptom relief should be all important, not just test results. Looking at your test results, your Free T4 is only at 30% of its range. The range is far too broad to be functional for many people and also, people may have different levels at which they feel best. So, just being in the low end of the range does not mean that all is okay for you. For best results Free T4 should usually be above mid-range. In addition you were tested for Total T3, not Free T3. Most all of Total T3 is bound to plasma protein and thus biologically inactive. The small portion not bound to protein is called Free T3. Free T3 is metabolized in all the cells of your body. A lack of Free T3 at the cellular level is what causes hypothyroid symptoms. Your Total T3 is only at 18 % of the range. If a Free T3 test for you shows a similar position relative to its range, then you need to increase your Free T3 level into the upper half of its range, as needed to relieve hypo symptoms.
Since you mentioned Hashimoto's, I assume you are on thyroid med, since your TSH is relatively low in the range. Is that correct?
Looking at your thyroid results you are still suffering from symptoms of hypothyroidism especially due to the relative low T4 and T3. I think you have trouble absorbing the thyroid pill which also warrants you to rule out other common deficiency by doing these blood tests.
Vitamin D3
Vitamin B12
Ferritin
Also concerning thyroid issues do a trail on natural dessicated thyroid (NDT) medicine instead of levothyroxine as your T3 levels are not adequate and this might be the reason why your hypothyroid symptoms are not getting better.
Before discussing your status, please tell us about the symptoms you have.