Is joking that causes psychological and physical harm to the family considered Haram, and what is its expiation if it is?

You have committed a grave error, and it is feared that this might be an act of disobedience (uquq) because your lie caused significant harm to your family. You must perform sincere repentance (tawbah nasuh), and strive to remove the impact of the fright you caused your mother and siblings by swearing to them and having your friends confirm that you are fine. Do not treat a sin with a greater one by abandoning prayer or intentionally breaking your fast. Contact your sick sister to assure her that you are well, and if possible, speak to them via video call so they can be reassured of your safety.