I am so desperate for sleep I could cry

actually...I do cry. But anyway, you guys...my 5 week old barely sleeps at night. I am starting to lose my mind wondering what I could do differently. He will sleep about two hours and then from 1:30Am or 2am he is just awake on and off for the rest of the night. Every single time I lay him down he cries. I might be getting three hours of sleep at night total. I usually end up coming downstairs and bouncing him in his bouncer for a majority of the night so we don’t disturb my husband. He will fall asleep there, but that doesn’t help me because obviously I stay awake while he sleeps there. We just bought the Love To Dream swaddle and it didn’t help. I am getting desperate. I only sleep on the weekends when my husband is off of work.