Aside from androgenetic alopecia, what are the likely causes of hair thinning/loss in younger women? which blood tests would be helpful in diagnosis?

Stress: Assuming you have tested for thyroid disease, the most frequent cause of hair loss in younger women is stress.

Fe, TSH..: Best test is to look at photo of your sisters and mother as unfortunately the diagnosis is likely androgenetic alopecia. Should probably check iron and TSH but they are likely normal. Make sure that the hair loss is non scarring and diffuse. The causes of patchy and scarring hair loss is quite different.