Hi congratulations on the job! I'm from the UK and worked for RCCL and I just went to my local doctor who couldn't believe the amount of tests they wanted done! So you'll be fine doing that, as long as all the tests are done. Hope that helps :-)
Just make sure you have the proper forms - there's one sheet that's your medical history and another that is the test results. Have the dr's office go over the results page to make sure you have ALL the tests. when you get to the ship, one of the first things they'll do is have the ship nurse go over the forms with a fine toothed comb to make sure they're all there. If not, you could be denied coming aboard, but lately they've been letting people on for a cruise and making them get the missing test in the first available port - which could be terribly expensive.