First of all, know that every working mother of a young baby goes through mornings like that...for many of them, every morning is like the one you had today.
As for being proud of having a baby...I have a slightly different way of thinking about this. It doesn't take any special skill or talent to give birth to a child. So you're right...simply having a child may not give a person a feeling of pride. Where the pride comes in is in your own work and ability in taking good care of the baby. The fact that you only sometimes have mornings like this is a testament to your ability to be organized, keep to a routine, and mother your baby well enough that he knows he will be taken care of.
Once he gets older, and starts walking, talking, etc., you'll begin to feel pride in his accomplishments. Until then, take pride in the fact that you are the main breadwinner for the family, hold down a responsible job, already have your figure back, AND you give your baby the very best care possible. That's a lot to be proud of!