Sleep schedules

I feel like a monster but I literally can not handle much more of my son's lack of sleep. The pediatrician said we're spoiling him and just need to let him cry but he has the WORST cry ever and if I have to let him cry it out I'll lose it. From what all my friends tell me his sleep habits are not normal and instead of improving they're getting worse. He'll be 1 month old on Saturday and for the the last 3 weeks he only sleeps for 2 hours at a time at night. Now last night and tonight he's up every 45 minutes to 1 hour wanting fed. When I feed him he eats until he's full so I can't feed him more to get him by longer. The pediatrician said he should need to eat more than every 2-3 hours. We were up for a feeding at 12 and again st 1 and now he's literally sitting in his swing grunting for the last 30 minutes. I'm not sure if there's something else that could be wrong or what. He's formula fed using a special preemie formula.