Once a creature becomes monstrous, it can’t become monstrous again. If the creature is already monstrous when the monstrosity ability resolves, nothing happens.

Monstrous isn’t an ability that a creature has. It’s just something true about that creature. If the creature stops being a creature, loses its abilities, or loses its +1/+1 counters, it will continue to be monstrous.

Chillerpillar gaining flying after it becomes blocked won’t remove the blocking creature from combat or cause Chillerpillar to become unblocked.