Vomiting within 15 minutes of a pill counts as a missed dose, so retaking it straightaway, as you did, was right. Since that happened early in this pack, your pill should still be working, but it's safer to use a backup method like condoms for the rest of this pack because of that one episode.
Next Steps
Your period usually starts within 2 to 4 days of finishing the active pack, so expect it around 29th to 31st Nov. Please use a backup method during 27th to 29th Nov too rather than relying on the pill alone, and check with your gynaecologist if you're unsure your cover held.
Health Tips
If periods don't arrive within a week of finishing the pack, take a
pregnancy test.