Dengue Fever: Given the patient's symptoms of fever, bodyache, rash, and thrombocytopenia, along with the geographical location of Puerto Rico where dengue fever is endemic, this diagnosis is highly plausible. Dengue fever is known for causing severe flu-like symptoms and can lead to severe thrombocytopenia.

Chikungunya: Similar to dengue fever, chikungunya is prevalent in Puerto Rico and can cause fever, bodyache, rash, and thrombocytopenia. The symptoms overlap significantly with dengue fever, making it a likely consideration.
Zika Virus: Although less commonly associated with thrombocytopenia compared to dengue, Zika virus infection can present with fever, rash, and body aches. Given its presence in Puerto Rico, it remains a possible diagnosis.
Influenza: While influenza might not typically cause thrombocytopenia, severe cases, especially in older adults, can lead to secondary bacterial infections or other complications that might result in thrombocytopenia. The presence of fever, bodyache, and rash (less common but possible) keeps influenza in the differential.

Meningococcemia: This condition, caused by Neisseria meningitidis, can present with fever, rash, and severe illness. Although less common, it is critical to consider due to its high mortality rate if not promptly treated.
Rocky Mountain Spotted Fever (RMSF): While more commonly associated with the southeastern United States, RMSF can occur in Puerto Rico. It presents with fever, headache, and a characteristic rash, and can lead to severe complications, including thrombocytopenia, if not treated early.
Hantavirus: Although rare, hantavirus infection can cause severe disease, including hantavirus pulmonary syndrome (HPS) and hemorrhagic fever with renal syndrome (HFRS), both of which can present with fever, bodyache, and thrombocytopenia.

Leptospirosis: This bacterial infection can cause a wide range of symptoms, including fever, bodyache, and rash, and can lead to thrombocytopenia in severe cases. It's more commonly associated with exposure to contaminated water.
Ehrlichiosis/Anaplasmosis: These tick-borne illnesses can present with fever, bodyache, and rash, and may cause thrombocytopenia. They are less common but should be considered in the differential diagnosis, especially if the patient has been exposed to ticks.
Viral Hemorrhagic Fevers (VHFs): While extremely rare in Puerto Rico, VHFs such as Lassa fever or Ebola (if the patient has recently traveled to an endemic area) could present with similar symptoms and are critical to rule out due to their high mortality rates.