All women should keep an extra pack of birth control pills laying around just inc ase something like this happens!
Yuo can ask your doc for an rx for an extra pack.
You would take the next pill in pack, or the same pill in a 'spare pack'.
You must take 21 active pills, and by throwing up one pill and taking the next, you are cutting your month short by one. It is not good to do this, it compromises protection.