I think what you are going through is totally normal. My baby was 37 weeks and cluster feeds at night to this day (he is 4 months old now). The first two months he way so sleepy at the breast, I used to strip him down and tickle his feet too. He would nurse, sleep, wet a diaper and repeat every 2-3 hours.
Stop supplementing with formula and keep pumping. Sleep when the baby sleeps. And nurse as much as you can. As the baby's tummy gets bigger, you will have longer stretches between feedings.
Good luck and hang in there!!!