I think you have no reason to feel guilty at all - you did all the things one would normally do on a birthday - cake etc.

3 hours is a looooong time to socialize with people when you kind of want to be by yourself. I think they were just trying to support you on your birthday. Don't feel bad because you've done everything right and got involved in the birthday festivities. Just because you then wanted some alone time - who can blame you? 3 hours ...... I'd be zzzzzzzzzzzzzzz