Yes you can wear your baby in a baby carrier on yourself while going through airport security.
I've seen several mothers and even fathers wear their baby in a baby carrier and go through security and once you pass through security the TSA agents may also swab your hands to test for gun powder or explosive residue.
There's no need to remove the baby from your body while going through security or when boarding the plane but when you get onto the plane you'll need to remove the baby from the carrier when taking off and landing or when flying.