3 week old won't sleep in bassinet, don't know what to do.?

My baby girl is almost 3 weeks old and she will not sleep in her bassinet or crib. She would only sleep on me but last night she rolled off (still on the bed but still scary) I'm terrified of something happening to her. Its not safe to have her on me. She will sometimes take small naps in her swing but not often and not long. We've tried swaddling, incline, white noise, one of my shirts, soothing her etc. I dont know what else to do. I'm terrified of SIDS and back is supposed to be best but she just wont accept it. We were able to get her to sleep twice in it but wrapped in a certain blanket. Only thing is its a large plush blanket and its not safe to have her sleep in it. Any help is greatly appreciated. I've asked her dr but they didn't offer any help he just said to try to get her on her back.