M.P.
If you don't take your pill like you are supposed to, you'll start your period in about 2-3 days from the last day you took your past pill. Like clockwork.
So yes it's normal in these circumstances. The only concern I would have is being off birth control. Are you using something else?
It doesn't seem likely that the BC was making you vomit. It's more likely a virus or something you ate.