If you already think your milk supply is overwhelming, then you'll want to hold off pumping for a while. When you pump, it tells your body that you need to make that much more milk since it's being expressed. On the other hand, having extra milk stored in your freezer will give you so much peace of mind later on. If you are okay with keeping up with pumping, then you may want to go for it!
The Lactation consultant told me to hold off on pumping for at least a month because it can effect your milk supply. I'd recommend hand expressing over pumping at this point
Re: Milk suply/ breast pump