Is it immature to be upset over this?

Bummer about your birthday.It's okay to be upset. However,you are on your way to maturity! Making choices and dealing with the consequences is a huge part of being a responsible adult. Take a chance on applying. Hopefully, you'll be able to have a 1-2 days off to celebrate without your new boss getting offended. If not, celebrate your birthday in Late November when Halloween in long gone. Since your brother works there maybe he can get you in then.