This is probably the "wrong" advice, but I had this problem when LO was around that age and i ended up propping pillows around me and sleeping with her on my chest. I was reprimanded by the pediatrician but I was just SO desperate for sleep.
LO is now 11 weeks and for the past few weeks I have been swaddling her and putting her in her crib. The first couple nights were rough but I can tell she is starting to feel more secure in her crib and getting used to sleeping on her back. And I sleep much better now. When I let her sleep on my chest I slept so lightly I'd wake up everytime she moved.
Point is, do what works for you. You need sleep and LO is too young to fall into bad habits. So whether it's co-sleeping or putting her in the swing to sleep, just do what works.