Synthroid and little bit

I have been a low dose of synthroid for 6 months now. My symptoms before syntrhoid were dizzy feeling - almost passing out - very light headed all the time - forgetful - heart palpitations - extreme foot pain - fatigue - moodiness - wanting to jump out of my skin. Finally, after 2 years found a Dr that wanted to check my thyroid. It's changed my life. Now the only feelings I'm having after starting synthroid - extreme hair loss and a terrible cough. That's really my question - has anybody developed a cough after taking this medicine. It only will last a little bit in the morning after taking it.