I will tell u tho at one point I did get pregnant on the mini pill but I had been on it for 4 years.
They call it the mini pill. It doesn't have the extra female hormone in it. Its the only pill I can take even not breastfeeding becuz the extra female hormone makes my headaches unbearable. The one I used was called errin.
Talk with your doc. Being that you are breastfeeding you are very limited to kind. I believe it has to be a pure estrogen based pill but I could be wrong. I never went on bc when I was nursing only because selection was limited and you have to be on top of it otherwise its inactive. Not like ref bc where you could miss a day and just take two the next to make it up.
I don't know about the breastfeeding part....but when I was on the pill...Yaz gave me beautiful even clear skin..... Maybe you could ask your doctor about those.