first off congrats on deciding to give your new little one the best start oissible
secondly, you need to NOT squeeze so hard, as you could damaga breast tissue, which you dn't wanna do.
as foir the milk not coming out fast enough, i am not sure what to tell you. maybe you could try massage and breast compression to encourage letdown a little more though.
renting a hospital grade is an option, but in general, the medela pis is the best pump out there, and has cycling similar to a hospitla grade pump.
what speed are you using? maybe you could alter that and have it help a little? also the suction level may need adjusted to be most effective for you.
also, some moms suggeats looking at a pic of the baby or sniffing a blanket or artricle of clothign etc and imagining that it is the baby at the breast instead of the pump.