There are lots of free hat patterns on Ravelry. You can also just search "Beanie button hat free pattern" on an internet browser and it should show up.
Estrogen isn't really something you need to worry about increasing. The levels fluctuate on their own based on your ovulation. Your estrogen level can give you a little insight, but...
It's best to cut a pattern with your measurements first so that you properly cut your fabric. You don't want to accidentally cut your fabric too small and end up...