3 and 1/2 months still not sleeping

EBF baby, has never slept more than 4 hours straight in a night and it's rare. Wakes every 2 hours or less to feed. Yes he is hungry and nurses well if we both end up staying awake for the full feeding. I am over exhausted and tend to fall asleep when nursing and only wake up right before the next feeding so when I lay him down he wakes and wants to eat again. We use a Boppy to help support him becuase he is a big baby and I have large awkward breasts. I can't seem to figure out how to get longer stretches of sleep. We have tried napping 2-x during the day because he gets over tired if we dont. I have tried expressing milk and bottle feeding him so he takes more, but it backfires because he doesn't like bottles much. We do have a set bedtime and I read his cues. He is tired anywhere from 8pm-9 and will be alseep by 9:30. He fights to go to sleep. He always has since he was 1 month old. Help me!! I am over exhausted and worried that my baby blues are turning into ppd if I don't get more sleep!! BTW his naps are normally 20-40 minutes. If I hold him I can get and hour or more. I've tried napping with him, but it's a fail. Either he wakes up or I can't sleep.