Doctors usually follow the path of least resistance...and when it comes to thyroid treatment this is doubly true. You said you are being treated with Synthroid...which I'm supposing is for Hypothyroidism?
Hypothyroidism is in most instances a by-product of underlying Auto Immune disease ...Hashimoto's being the most prevalent. Inflammation from Hashimoto's disease, also known as chronic lymphocytic thyroiditis, often leads to an underactive thyroid gland (hypothyroidism). Hashimoto's disease is the most common cause of hypothyroidism in the United States.
Please speak with you prescribing doctor, and try to get them invested in getting a full panel done, including your hormone levels, antibodies etc... Synthroid will maybe level out your TSH readings, but you may have a conversion problem.....Meaning that the T4 you are taking is not being converted at a cellular level to the T3 that your body needs. Hypothyroidism and Hashimoto's are a balancing act ...Optimal treatment being the ultimate goal.