My baby is 4 days old & I'm feeling so emotional I cry about everything...is this normal?

I was just fine in the hospital, but my first day at home I just started crying because I felt so happy & blessed to have a healthy baby. Then later something my husband said pissed me off so bad I started crying and yelling at him. I feel like my emotions are going crazy! I also feel so attached to my baby I don't really put her down I hold her all day & she sleeps in the bed with us at night. I almost feel lonely if she is not with me. Is this normal after having a baby?