Is it possible to pump to much?

Sometimes right after I finish pumping my son wakes up and wants to nurse and then he pulls off and cries during. I know there still milk in there cause I can squeeze it and it squirts out. Maybe it's just harder to get it out? I've been trying to up my supply so I pump about 30 minutes every few hours. I want to donate my milk to babies in the nicu and nurse my son. I just think it would be amazing to help other babies with my milk (i have 100oz so far!) but not if it takes away from my son. Is it possible that I'm pumping to much out?