Aw, your baby is so young! That is so very normal at that age. You can't spoil a three month old baby no matter what. Mine clung to me most of his infancy. He went through a daddy is awesome phase around 12 months, then started clinging to me again after a few weeks, then just recently he has started literally pushing me out of the way to get over to daddy. Or to get to grandpa. Or to get to the neighbor. Or to get to that cute teenage girl walking down the street. Seriously, he loves making friends with everyone. Clearly my "spoiling" him by not letting him cry by himself has not interfered with his independence. Of course every baby has their own personal disposition, but I think that attentive parenting provides every baby with the security and confidence to do and to be whatever suits their own disposition best.
K. Sophia - Mama to my little lactivore, the amazing Mr. X (11/10).