Ce que j’ai honte ! is equivalent to Random’s comment comme j’ai honte !. See the tlfi ce entry (II.B.1.) .The person speaking is personally embarrassed. (I’m so ashamed!)

With comme c’est embarrassant !, the person speaking is telling something is embarrassing but might not be affected personally. (How embarrassing!)

Finally, with quelle honte !, the person speaking is upset by someone else’s behavior. (What a shame/disgrace!)