From "Diagnosis and Treatment of Hypothyroidism: A Patient's Perspective, ref. 104 on iron deficiency (ID),which is the most common and widespread nutritional disorder in the world.
"CONCLUSIONS:
It appears that for the diagnosis of ID, a cutoff of 100 μg/L for serum ferritin concentration should be considered in most conditions and 20% for TSAT, except in particular situations, including young healthy women with heavy menstrual flow. New indications of intravenous iron supplementation are emerging."
https://www.ncbi.nlm.nih.gov/pubmed/26561626
I expect that you are going to need a number of increases yet. Most people seem to need to take 2-3 grains (120-180 mg) to achieve symptom relief. So I suggest that you should try to get back in to see the doctor, get new tests and a dose increase as soon as you can. Your serum T4/T3 levels will reflect over 95% of the total effect of the med increase in about 5 weeks, so a month from now would be a good target for the next appointment.
Have you had any additional dose increases? Have you been tested for Vitamin D, B12 and ferritin?
One of the best definitions I have seen for hypothyroidism is "the clinical state of suboptimal T3 effect in some or all tissue in the body". So it should not be a mystery why you are having hypothyroid symptoms. Your FT4 and FT3 are at rock bottom of ranges that are already far too broad, due to the erroneous assumptions used in establishing those reference ranges. Just being anywhere within the so-called "normal" range does not mean results would be optimal for you. Plus there are many other variables that affect the RESPONSE to thyroid hormone at the cellular level. There are numerous studies that show even in the untreated state TSH has only a weak correlation with FT4 or FT3, and a negligible correlation with symptoms (TISSUE T3 EFFECT). Also, FT4 and FT3 have only a weak correlation with symptoms. So, there are no reliable direct measures of a person's TISSUE T3 EFFECT, which determines thyroid status. The best indirect measures of your thyroid status are an evaluation for symptoms that occur more frequently with hypothyroidism, supported by tests for Free T4 and Free T3.
In the treated state, studies have shown that many patients taking thyroid hormone will have suppressed TSH levels. Studies have also shown this to be a result of taking the full dose of thyroid hormone only once or twice daily, which establishes an equilibrium among TSH, FT4, and FT3 that is quite different from that with the usual continuous low flow of natural thyroid hormone in the untreated state. So, a TSH test is even less diagnostic in the treated state. TSH-deficiency has no pathological effects. A suppressed TSH in a treated person does not indicate hyperthyroidism and the need to reduce med dosage unless there are attendant hyperthyroid symptoms due to excessive serum levels of FT4 and FT3. So TSH should not be used to determine thyroid hormone dosage. Instead the patient should be treated clinically, to relieve hypothyroid symptoms, and to optimize other important areas such as cortisol, Vitamin D, B12, ferritin, and Reverse T3 (if initially found to be excessive).
So it is good that your doctor increased your dosage. Most hypothyroid patients taking NDT (desiccated) thyroid med need between 2 and 3 grains (120 to 180 mg) in order to relieve hypo symptoms. The final amount should be determined by relief of symptoms. At your age, you should try to get an increase every couple of weeks up to 1 1/2 to 2 grains, dependent on body weight. Then after 8 weeks, further increases should be determined by a re-evaluation for symptoms and tests for FT4, FT3 and TSH.
Regarding your question about changes in FT4 and FT3 level, do you take your thyroid med in the morning before blood draw for tests?
When did you increase to 60 mg? What symptoms do you have?
Update: upped to 60 mg desiccated thyroid