Your FT4 is extremely low in the range, indicating that you might need an increase in med, since you have a TSH of 37+. Your FT3, also has room to come up, since it's at 61% of the range. You might ask to try the 25 mcg/day, rather than just 4 days/week.
Which antibody test was done? There are 3 of them, two will diagnose Hashimoto's, which is associated with being hypo, but can present with periods of hyper. The other (TSI) is definitive for Graves, which is associated with being hyper.
Free T3 2.94 (1.71 - 3.70 pg/ml)
Free T4 0.83 (0.70 - 1.48 ng/dl)
Antibodies 27 IU/ml (19 IU/ml)
Theses are my test results
Wow - your doctor has you on quite the roller coaster ride, doesn't he? As long as you continue on and off med, your levels can't stabilize and you shouldn't conceive, because adequate thyroid hormones are essential for the growth and development of a fetus.
TSH is a pituitary hormone and should not be used, alone, to determine thyroid hormone status. What were the actual levels of T3 and T4 and were they "free" or "total"? Tests for total T3 and T4 are considered obsolete and of little value.
Please post the T3 and T4 results and be sure to include the reference ranges, since these vary lab to lab and must come from your own report.
Free T3 and Free T4 are the hormones to be concerned with.