I have no idea, and frankly I'm not in the position to be giving advice about zinc deficiency, especially when you've not used finasteride, and are having severe problems because of zinc deficiency. I've no experience with that, and you should consult your GP.
Regarding hair loss; you might be a part of the evolution, which means that you may experience worse symptoms of androgenic alopecia than anyone else in your family. Certain factors may accelerate things. Me for instance, I've been having a problem with scalp seborrheic dermatitis for almost 10 years, before a doctor identified the condition when I went to see one because of my diffuse thinning. I needed strong steroids to get it under control, and I need to use Nizoral every day for maintenance. My scalp condition was bad, and I lost a lot of hair from scratching. My brother show signs of diffuse thinning too, but I'm the only one who sees it, yet. He doesn't have any problems with his scalp. My condition, definately accelerated the progress.
To know what progress to expect, you need to evaluate at least your father, your mothers father, and her grandfather on mothers side. Take a look at her brother(s) too, if she has any. Find the worse case.