Please Help - Can't get him to sleep

Angela
I am going CRAZY! My little one is 5 weeks and will not sleep anywhere but on me. I have tried swaddling, turning lights off, letting him cry ( I don't believe in the cry out method but I've left him for no more then five minutes to see if he would calm down). I know having him sleep on my chest in bed isn't safe but I don't know what else to do. Sometimes he will sleep in the swing but I heard that isn't safe either. Please help. He wants to be held 24/7. I'm an EBF. I thought that info might be helpful. I am considering buying a rock n play. I'm willing to try anything. I have 6 more weeks of maternity leave. I would like to get him sleeping on his own by then. Any help and tips would be greatly appreciated. Thank you.