Everyone is different in their need for thyroid hormone, so just being anywhere within the range does not mean it is optimal for you. Before further discussion, please post all your thyroid related test results and reference ranges shown on the lab report. Also, is the blood work from the time you were on 100 mcg of Levo or 137? Even more important are symptoms. So please tell us about all symptoms that you have currently.
I should have also asked if you took your thyroid med in the morning before the blood draw for those tests.
How long after taking the Levo was the blood draw?
Also, please post the test results and reference ranges and tell us about any symptoms yoj have.
Thyroid med should not be taken until after the blood draw, in order to avoid false high results. Taking that into account your FT4 is only at 40% of its range. Your Free T3 of 3 is only at 12.5% of its range. Since you still have hypo symptoms, those levels are too low for you. Also, your body is not converting the T4 to T3 needed by all the cells of your body. Inadequate conversion of T4 med is quite norma for patients on T4 only. TSH is not a useful tet when already taking thyroid med. Most times when patients are taking adequate thyroid med, TSH is suppressed, which is not an indication of becoming hyper, unless there are hyper symptoms due to excessive levels of Free T4 and Free T3. I mention this only because most doctors don't understand this and will respond to a suppressed TSH by erroneously reducing med dosage.
If you are able to get your doctor to prescribe T3 type med, you should ask him to increase your T4 med slightly, and add some T3 as needed to gradually to raise your Free T3 above mid-range, as needed to relieve symptoms. I say this because symptomatic change is mainly related to Free T3, and less with Free T4, and negligibly with TSH. If you need to convince your doctor of this, use this link and scroll down to Fig 1C and click on it and you will note the effect of different levels of Free T3 on the incidence of symptoms.
If your doctor refuses to treat clinically, as needed to relieve symptoms, then you will need to find a good thyroid doctor that will do so. In addition, hypothyroid patients are frequently deficient in Vitamin D, B12 and ferritin. D should be at least 50 ng/ml. B12 in the upper part of its range, and ferritin should be at least 100. If not tested for those you should get those done and then supplement as needed to optimize.
If you want to confirm any of this, click on my name and then scroll down to my Journal and read at least the Overview of a paper on Diagnosis and Treatment of Hypothyroidism: A Patient's Perspective.