Hair loss/thinning remedies...?

I had my baby a year ago and like a week afterwards my hair just started to thin drastically. Think handfuls of hair coming off everyday in the shower. I got a shorter haircut and things got a little better for awhile (why is that? What is it about short hair that keeps you from thinning?). But a few months ago I changed my diet a bit to lose weight and now Im back to shedding enormous amounts of hair.

Has anyone found something that helps with this? I started taking iron supplements and that’s helped a bit - I think that it has something to do with my borderline anemia and weight loss. I’m wondering if there’s more that I can do that’s not too invasive...