Should Synthyroid Dosage Be Increased While On Birth Control Pills?

Hi,
I had a thyroidectomy about 12 yrs. ago and I have been taking synthroid since then. My tsh is about 1.5 and free t4 is about 1.6 consistently. But, if I take birth control pills, the free t4 is about 1.6 which is normal but my tsh varies between 8 to 11 which is bad. I separate the synthroid and birth control pills by 12 hrs. I read online that this is because of estrogen in the birth control pills? Do I treat myself based on the free t4 or tsh or is there any other test that will be help me more understand this? If I need to increase the synthroid dosage during the duration of birth control pills, how much percentage should I increase it? After the birth control pills are over, should I decrease the synthroid dosage than regular dosage? Thanks.