Middle of night fussiness

J❤️
My lo ussually wakes up for a feed some time between 3 and 5 am. Always varies. She's 13 weeks btw. So she will wake up and start fussing a ton. I've let her lay for a little to see if she will go back to sleep but she will just keep tossing or start crying.  So I pick her up out of the bassinet. Feed her. Hold her a few mins upright( I don't burp since this will wake her up fully) . Lay her back down. I don't say anything, lights are off, I only feed, hold a few, lay back down. Ussually I do make the shhhhh sound but that's it. Though regardless she will just either wake up right away, or she will lay there fussing and tossing and turning for over an hour (unless I I un swaddle her and bring her in bed Wich I don't want to do that early) I don't get a good rest with her in bed so I try not to bring her in until after 6:30/7 am. Sometimes the fussiness happens twice. Around 3 and again around 5:30/6. Does anyone have any suggestions on how to either get her to sleep longer or to get the fussiness in the middle of the night to go away? I try gently rocking the bassinet but doesn't help. I have a white noise machine on and I have the shusher I use. Truthfully id really like to get more sleep but since she ussually will fuss for over an hour I don't get sleep past 3/5 am. Please give advice how to kick this middle of night early morning fussiness in the butt. I don't know what else ...