Breastfeeding help

Hey ladies! So my son was in the NICU (due to my autoimmune disease) being observed and he was given formula. He'll be three weeks on Wednesday I've been pumping a and bottle feeding. I have tried to get him to nurse and we've had success with a shield. He will nurse for 10-20 mins. My question is why do we both end up wet with milk?!? lol I know he lets go a lot like he can with a bottle so it leaks and he always has it all over his face. A couple friends said maybe it's coming out faster than he can drink it. We use slow flow nipples with bottles because he will inhale it and then have hiccups and gas and spit up. I would love to exclusively nurse and bottle feed as back up my freezer is already stocked with milk I'm blessed in that department.