I feel so embarrassed

Life is full of cringe-making moments, but most of the time, most people are far to involved with worrying about how they look to others to be all that concerned about things that you believe make you look silly.

For whatever reasons, she did what she did. She had the right to do that, and you have to accept that people will change their minds and they will disappoint you. Sometimes they do that for perfectly logical reasons (even if we don't know them), and sometimes they flip-flop for reasons even they don't understand. Sometimes they do it deliberately for malicious reasons, but I think the most positive way to deal with people is to assume the best of them until they present clear evidence that they're an asshole.

I suggest you do your best to let this be and move on. The next time you see the girl, behave as if she never agreed to do anything. Definitely do not take the attitude that she let you down and didn't give you something you're entitled to.

Worst case scenario, she thought you were a creeper and said yes to keep you predictable, best case scenario she just forgot she made plans already

That will probably be forgotten in like a day, it’s a very minor thing that you shouldn’t worry about.

Sounds like she wasn't being honest with you. It's best to forget this incident and move on.

She decided to fuck him instead.

HOWEVER, bottom line she said no. Who's to say, what her reasoning, you may never kknow. But she said "no", you may not like it, but accept it. She had her reasons, maybe she chickened out at the end. Question it ?- sure. If you want to keep digging at the open wound. Just drop it, let it go and move on.

I don't get the full context of this situation. So, my guess is that she probably had plans already and that intervened with what you had planned for her. Or, Maybe this could be a big misunderstanding. It's best to talk to her so you can understand what fully happened.