Flecainide is one alternative - but I believe it is contra-indicated if one has other heart problems. Amiodarone wiped out my dear old dad's thyroid when he was alive - nobody thought ever to check his thyroid while he was on it.
When my husband got atrial fibrillation and his Cardiologist wanted to put him on Amiodarone, I was well-versed enough to question the decision and he went on Flecainide instead. From the research I did when my husband had AFib (since cured with ablation), I was given to understand that Amiodarone is often used as a last-ditch attempt when other avenues have already been pursued. Flecainide is a better option if you can take it.
Amiodorone is a very powerful deiodinase inhibitor. Deiodinases are the enzymes that catalyze the conversion of T4 (the "storage" form of the thyroid hormones) to T3 (the "active" form). Amiodarone has a very long half life, so it stays in your body long after you stop taking it.
I have no idea what the alternatives are to amio from a cardiology point of view, but I'd certainly ask my doctor if there is an alternative.
Are you getting treatment for your thyroid?