Uncontrollable Leaking

Alexis • 3 year old Chloe💖 11/15/15 & Jacob 💙 3-5-19
I'm a FTM, my baby is 11 days old. When I breastfeed which ever side I'm on the opposite side leaks. I haven't mastered how to pump & feed simultaneously so I just make a mess. Does/ did this happen to anyone else? Does it go away after a while? I can't imagine in 9 months being at the zoo feeding her & trying to pump on one side. See my point? Any suggestions on how to stop the leaking?
I have nursing pads I leak so much I'll leak through them and on my clothes soaking my baby & myself.