Without even getting into the discussion about different birth control pills, I can tell you that I would bet my last dollar that having been diagnosed as hypothyroid from Hashi's, a levothyroxine dose of 75 mcg did little to nothing for you and that your biologically active thyroid hormones (Free T4 and Free T3) remain inadequate. When not being treated adequately you cannot know whether the problems are due to continuing hypothyroidism from inadequate Free T4 and Free T3 or the birth control pills.
The reason I am so confident about this is that when starting on thyroid med, in response the body will react by reducing the pituitary output of TSH. This then reduces stimulation of the thyroid gland resulting in reduced output of natural thyroid hormone. Since serum levels are the sum of both natural thyroid hormone and thyroid med, only when med dosage is high enough to essentially suppress TSH, will further dosage increases start to raise the levels of Free T4 and Free T3. A recent, excellent scientific paper concluded that: "Hypothyroid symptom relief was associated with both a T4 dose giving TSH-suppression below the lower reference limit and FT3 elevated further into the upper half of its reference range."
So several questions need to be answered. What, if any, symptoms do you have besides those related to your periods? Also, please post your current thyroid related test results and reference ranges shown on the lab report. If tested for cortisol, Vitamin D, B12 and ferritin please post those as well.
Lab test results and reference ranges shown on the lab report?