4 month old and hardly any sleep

Bridget

My baby girl just turned 4 months at the end of November and we still struggle with bedtime and sleeping in general. I’m a FTM and I feel like I am just not doing something right. She was a preemie, born at 36+3, so I have been basing everything off of her adjusted age for milestones and sleeping and such. Her naps are only 30-55 minutes long and she seems to need a nap every 1-1.5 hours but at night it’s a struggle to keep her asleep. I track on this app and it says she’s only getting 12-13.5 hours everyday and I just feel like that’s not enough. She wakes multiple times in the night and will wake every hour or so. My night pretty much goes feed, put back to sleep, I’m already up so pump for 30 minutes and by time I lay back down she is awake again and needs rocked back to sleep. I’m getting maybe 3 hours of sleep at night with my days pretty much starting at 4 am since I’m not able to get into bed until around midnight. I’m just tired. I don’t know how to keep my baby sleeping for naps or bedtime. We got the go ahead for rice cereal since she is 4 months. Will that maybe help her sleep longer? Any advice is appreciated.