Mommmmy!!! I felt the same way. And the nurses and lact consults kept saying it takes a few days, give it time, be patient and guess what!! After 3 days i was a leaky faucet. My son was born 6lbs 11oz and day 12 hes a whopping 8lbs. So worry not...it will come.
Your milk hasn't came in yet. In the meantime your baby is getting colostrum from your breasts. Which is just as good as the breastmilk, and it's very important for them to get the colostrum and yes it will fill their tummies up. In the next couple of days your milk will come in! It doesn't happen right away.