My old belly-button piercing hole has semi-solid, white pus coming from it when I squeeze and is red - had baby 9 days ago. Do I need to do anything?

Sebum. Do not put anything into the piercing. Wash in shower. See a DR if it is very sore or swollen. Avoid bacitracin, neosporin, triple antibiotic as these will do no good and are common sensitizers.