Most Helpful Girl
I'm sorry. Maybe she's not comfortable with it? Maybe she doesn't want to get too attached to you? Do other people know that the two of you are dating?
There can be plenty of reasons for why she won't. I don't think she is embarrassed. If she was she wouldn't have said yes, right?
Tell her exactly what you told us. She'll understand :) Ask her why she won't be affectionate in public, if something is wrong. I'm sure everything will be okay. Good luck