Does biotin or iron deficiency cause permanent hair loss?

This is difficult to answer without an in-person evaluation. I suggest seeing a hair loss expert now to evaluate and go over your condition and provide you information about your best treatment options. There are great non-invasive options like prp/progesterone and/or hair transplantation. See an expert. Best, Dr. Emer

It probably would, but it depends on a variety of factors. Without more in depth history it's impossible to say for sure- if for example you were already prone to receding due to family history, etc. it may be that the vitamin deficiency sped up your normal balding process and some hair is gone forever now. 

Biotin deficiency is not a common cause of hair loss. So for most people, taking biotin is not useful at all. Iron deficiency can cause hair loss...but it's far less common than many would currently believe. But if iron deficiency truly is the only problem a patient has, there is a high chance that all hair will return. It's not a 100 % guarantee though since things that cause telogen effluvium can accelerate the development of androgenetic alopecia. See a dermatologist or hair specialist if concerned about your hair. Your hair loss may be more complicated than simply iron and biotin.