If I were you I would not give up on getting tested. I went to Aruba for a week in 2008 and started feeling sick toward the end of my trip. I came back and got progressively worse symptoms (which included those listed by you). Two months later I was diagnosed with Lyme disease. I know of two other people that have gotten sick while in Aruba or on their way back from Aruba that have been diagnosed with Lyme disease.
It is my understanding that Leptospirosis, another spirochetal bacteria, is also present in the freshwater of some Caribbean nations. It may or may not be symptomatically similar to Lyme. I have not researched the issue.
If your doctor believes that only deer ticks carry Lyme, then I would seek advice elsewhere as he or she is truly ignorant. Per the Center for Disease Control's website, "The Lyme disease bacterium, Borrelia burgdorferi, normally lives in mice, squirrels and other small animals." Additionally, some scientists believe that Lyme may be transmitted by mosquitos as well as by ticks.
Please don't give up on a diagnosis!
Best of luck to you,