Can Medication For Thyroid Disorder And Depression Cause Hair Fall?

Would thyroid medicine have an effect on my hair? My hair has been falling for out for about five months . I was put on thyroid medicine about two months prior. I have also started having dark hair growing in my white hair. At the same time I started on thyroid medicine, an antidepressant venlafaxine X-RAY 37.5 mg was added to my antidepressants I was taking.