Your words remind me of how DH and I felt when Ryan came. We had to stay in TX for about 2 weeks after he was born for ICPC and such to clear. Midway into the second week, DH looked at me and said "Do you feel like 'hey, this has been fun. When are his parents coming?'" Yep.
I didn't really feel like Ryan was 'my' baby until his first shots - that nurse made my baby cry and I nearly decked her. Mind you, I've worked in the medical field for `16+ years, including time working in a pediatric ER, so you think that wouldn't have bothered me so much. Except that was MY son's REAL tears. The nurse got out fast.
It took a while after that before I stopped being fearful that someone in the mall or in a store or somplace was going to point at me and shriek "That woman is not that baby's mother!" even though Ryan and I resemble each other strongly (many people thought I was his bmom's mother or older sister).
Hang in there. If anyone hasn't told you yet, newborns are HARD. They are not those sweet cuddly babies we all see - those are older infants. His first 4-5 weeks were the hardest, when it seemed like he didn't even acknowledge my existance, recognize me, etc. If you find yourself feeling that you hate this, that it's not working, that you're the worst mommy ever than remember that it will get better. Promise.
Hang in there.
Regina