My belly button has popped out during my pregnancy. Now it's four months after I delivered but why still my belly button didn't go inside.?

Longer leash. Before your pregnancy, your belly button was tacked down on the inside to a ligament (which used to be the umbilical artery and vein) from your umbilical cord when you were born. The degenerated artery and vein- now ligament- delivered blood to your liver. During your pregnancy that ligament stretched and probably tore so that the internal pucker is no more.