Worried about taking birth control...

So I've had my NuvaRing waiting for me for weeks now...I'm 9 weeks post partum and still haven't taken it. My concern is that I'm exclusively breastfeeding and that it might affect my milk supply and/or the baby. I didn't even think to ask my doctor when she asked if I want to be on birth control and what kind. But when I went to insert it the other day I just stopped dead in my tracks and got worried all of a sudden. I mean, why wouldn't the doctor have said something if it wasn't safe for breastfeeding moms?? Any mamas who are EBF and using NuvaRing (or any estrogen birth control) out there?? I need to know if you exoerienc d any side effects like lower milk supply. And what do you take for birth control instead??