Em, are you in touch with your child health nurse or a GP who you feel comfortable with? Please go and have a chat with them about how you're feeling.
Yes, sometimes babies are like this, and yes it does get better, but it sounds like you could really do with some extra help right now. There's no need to feel like you "should" cope better, everybody needs help when they have a baby. What help and when differs, but everyone needs it.