HI !
I had gone through your question and I understand your concern .
Yes your thyroid gland effect your heart , hormons produced by the gland changes your heart rates .
When the thyroid gormons are high , patient exsperience fast heartbeat .When the hormons are low they have slow heart rate.
The drugs that you are taking help your thyroid gland to have more
iodine but sometimes they cause the opposite effect -
hyperthyroidism .This happens when you take high dose more than you need .
I would say to check how much iodine you take with these 2 drugs , (DON'T forget also the Iodine you take from food ) .The amount you need is 150mcg/day
Check your heartbeat different times of the day ( be sure it's not any kind of stres that cause racing heart ) .
Check your hormone levels .
I would recommend to ask an appointment with your local doctor so you can discuss for the changes.
Wish you good health!