Is it possible that you had a supernatural experience? Sure. We'll never rule them out completely, because there are an infinite number of mechanisms we can and can't imagine by which they could happen. Is it likely, though? Probably not, because the number of possible natural explanations is just as large.
You heard a screech, and then saw your cup flying across the room as if thrown. My first thought is that it was thrown, or at least struck, by a wild animal who got into your room. If you didn't have the fan or the air on, you probably had the window or the door open. If not, perhaps it got in earlier, and escaped when you ran out to your father. Would you have noticed as you freaked out? (Possible test: describe the squeal in detail on a wildlife forum as if you heard it outside, then listen to the suggested animals on YouTube and see if they ring a bell.)
Coming up with natural hypotheses is fun, but considering the supernatural alternatives is fun too. Say the cup was deliberately thrown by a ghost or other ethereal entity. (Note: the "aether" is actually a long-discarded scientific concept, not just a story.) Why? And why only once? Did you manage to discern some sort of message from the action? Did the cup have any significance, or the place it flew to? Since the entity would probably realise you didn't get the message, why didn't it try again?
I applaud you for the wealth of good skepticism you've already applied to this event. I know it's frustrating when you're still left without an explanation, and the prospect remains that you'll never really know. I hope I've made you a little more optimistic that there is a natural explanation to be had, even if you don't find it.
Good luck in any case.