Talk to Gynecologist on Hypothyroidism And Palpitations

I have an autoimmune disorder Hashimoto's since a year. I was diagnosed when my antobodies were >1000 and TSH was 62. Now i m taking 2 thyroxin tablets daily and my TSH is under controlled. Somedays I forgot to take my medicine and I feel like my symtoms are revived. Is it possible or is it just my assumptions? Secondly my heart rate stays so high since I got this disease. It stays between 100-120 or above. Dr. suggested me to take inderal thrice daily. But I have heard that palpitations are common in hyperthyroidism and people with hypothyroidism have slower heart rate. Why is it my heart rate is so high? I am tired of my heart beating so fast. It makes me tired all the time. What are the long time consequences of high heart rate?