Are you travelling on the 11th until 23rd november.
You need to fill in the visa waiver form on the flight to New York to get into USA. If you have a normal British passport there is no requirement for visas for any places you visit [except Bahamas where they give you a form to fill in on the ship]. Your T/A should really answer this sort of question.
We are going on the 9th nov. is this your cruise on the explore.