How long have you been taking the levo/synthroid? What dose are you on? Did you feel any of these symptoms before you began the medication?
I began taking synthroid eight weeks ago for my hypothyroidism. I was started out at a 137 mcg dose, and within 2 weeks I was feeling very anxious, had heart palpitations, chest pain, and I was starving all the time! I went to an endocrinologist who said I started out on too high of a dose. He cut my dose in half and I am still adjusting to the new levels three weeks later, but definitely feeling much better.
Also, each pill of the thyroid hormone medication (synthroid/levo) stays in your system for 7 days. Once you are on a regulated dose, it can take up to 42 days for your levels to report accurately on a blood test. Similarly, if you stop taking medicine, it can take 42 days for it to leave your system.
some patients need a slow titration starting with a small dose -- would re-evaluate the need (ie, severity of hypothyroidism) then start low and go slow to help your body adjust to the medication.