If you have already sworn in to a branch of the military but while you are on delayed entry you find out a parent is dying can you get out of the military to care for a sibling?

Yes, there is a discharge once you are in to allow you to care for family members given a family crisis situation. Given your situation, you need to talk to your recruiter with specifics and proof. If he tells you know, I would call his boss. However, you do need proof.