My wife taking Eltroxin 50 mg at every morning with empty stomach...

My wife taking Eltroxin 50 mg at every morning with empty stomach since two month back, as her TSH found higher (7.5 unit instead of 0.5 to 5.5). Recently it has been observed that, she is loosing hair too much. I just want to know, whether this increased rate of hare fall is the side effect of Eltroxin or the effect of high TSH? If the reason is first one then how the preventive step is to be taken? And if it is due to later, then why the medicine not doing the work properly? Please suggest the way to proceed.