In a 75-year-old woman admitted for LLQ pain, fever, and nausea with a presumptive diagnosis of acute diverticulitis, initial treatment with antibiotics, bowel rest, and IV fluids is initiated. However, despite this management, the patient deteriorates with continued pain, increasing fever, and rising WBC count. What is the suspected complication or problem, and what additional diagnostic and therapeutic steps would you consider to address the patient's worsening condition?