Baby throws up after feeding

My baby is only 4 weeks and she likes to only lay on me 24 7 so I can't get anything done and if I feed her formula she throws it up afterwards. Then after she throws up she acts like she's starving and wants to eat a bunch. Not to mention when she lays on me she wiggles around like she's looking for my breast. I couldn't breastfeed her because she would just cry at my breast and everytime I'd try I'd get frustrated and cry myself. I feel like I haven't slept since she was born because she gets separation anxiety and cries like she's being murdered if I put her in her bassinet. My bf is a huge help but he has to go back to work soon. I have headaches everyday from her screaming. I feel like a complete zombie I miss sleep.