Breastfeeding Help Anyone?

She is 4 days old and I am breast feeding. She latches well and she ate for hours at a time while in the hospital. My breast milk just came in and now she eats smaller amounts at a time many different times. She still seems hungry and frustrated even though I feed her on demand. I could have just finished feeding her and she unlatches on her own but seems frustrated and hungry again. I do burp her after and make sure her diaper is taken care of. I don't know what is going on. She also has been coughing/ I think spitting up while breast feeding. Usually near the end of it but sometimes during. I'm starting to get worried. Can anybody help?