Your plan of waiting a few days is a good one, don't try to force her to talk to you. Not replying doesn't mean she doesn't want to talk to you, it could be her way of signalling "this is the end of the conversation for now, talk to you later", but it could also mean that she doesn't know how to reply to the "self-loathing" message you sent her. Different people have different social cues. Give her some space, first and foremost. You've only just met after all.
When you want to ask her out again, don't start with "Oh, hey, want to do this together?", start with something like "Hey, how are you?". Have a conversation first. You don't want to come on too strong and put her on the spot, or seem desperate for her attention.
Honestly, I think you're worrying about it too much. In the meantime, try distracting yourself, or force yourself to stop checking your phone every few minutes. It's only going to stress you out.
Hope it goes well. Good luck!