HELP!!

My 6 week old daughter will only fall asleep when shes being held chest to chest. If we're not holding her and if she gets fussy the only way to calm her down is to pick her up or lay her down on her belly. To get a break I do let her fall asleep on her belly right next to me on the couch. I constantly am checking her because I know this is NOT safe. My question is, how can I get her to calm down without doing this? She doesnt liked being laid down or put in her swing. I've tried letting her cry it out but she'll just scream her little head off and have tears covering the sides of her face. Helppppp