I had the same issues you cited with my baby. He would fall asleep after 5 minutes and never get a full feed. As a result, he would wake up hungry after 15-20 mins and I would need to try and feed him again, only to have him fall asleep again! It was really frustrating. That led me to exclusively pump after one month. Exclusively pumping was really depressing for me because I felt like I couldn't spend time with my baby while I pumped even though I double pumped. It was hard to hold my baby while pumping. And I was constantly pumping in order to up my supply. It just felt miserable...but it was better to have breast milk for my baby rather than go all formula. For me, the pumping experience was the least fun out of all the motherhood duties, but the thought of giving my baby what he needs kept me motivated.
It's tougher than breastfeeding directly in my opinion because you lose that time to bond. And it's 20 minutes each pumping session, 8+ times a day. You should not feel like you failed; if anything, it's another challenge you've overcome as a new mother.
Google ivillage and exclusively pumping for great forums on how to handle EP'ing.
Good luck!!
FYI, I also used pump in style with pumping bra. You have to massage your breasts while you pump to drain breasts and get all the milk out, which is the best way to increase supply.
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