Thank you for your query at DoctorSpring.com
I am a little doubtful about your history. Do you have thyroid disorder?
Taking Levo thyroxine without hypothyroidism will cause thyrotoxicosis, which can cause heart rate to increase abnormally, abnormal rhythms in heart, bone and muscle loss, and weakness. anxiety and restlessness, sleeplessnes, and diarrhoea.
Hydroxycut, like most other dietary supplements, the effects are debatable. But it has been promoted well and seems to be helping. So you can try that out. But without hypothyroidism Levothyroxine will be harmful.