Hi, I have been given Loestrin 20 birth control pill, but I have mild alopecia and so told the nurse I wanted one low in androgen. However she has given me this, but apparently Loestrin is high in androgen and can cause hair loss? Is this the case?

The issue at hand, is what is the cause of your alopecia? There are different causes. Hormones is only one (although the more common one)
If this is a concern go see the doctor who ordered this and see about other options.