How old is s/he? If baby is 6 months or younger, you cannot spoil him or her. Picking up and carrying the baby will make your baby feel secure. There's also evidence to suggest that babies whose mothers picked them up, held, snuggled, etc. their babies when they cried ended up being more independent, confident and generally happy than babies whose mother's pass them off to somebody else, or leave them when they want mommy. Have you looked into getting a sling to hold your baby in?
It's totally normal for a baby to act that way (only wanting mama), so it's not just your baby! I understand though that it can wear on your nerves if you're constantly in demand by your lo, but try to be patient. It won't be long before that baby doesn't want to be held or snuggled by you so much!
Whiskers