Forgot My Friend's Birthday...

So yeah, today is my best friend Rachel's birthday. She mentioned it last week, but I totally forgot about it until this morning when she posted her cake on Instagram with a big #HappyBirthdayRachel hashtag. I feel terrible because we always make fun of people who forget birthdays at school. Now everyone knows I did it too... How do I even go to class today? Should I just pretend nothing happened? What if Rachel tells the whole world in front of me? Or worse, what should I give her as a belated gift? Any ideas and advice from anyone out there are appreciated. I'm so embarrassed but also curious about how others handle stuff like this...