Acalculous cholecystitis with bacterial infection: Given the patient's presentation with high-grade fever, chills, and ultrasound findings of acalculus cholecystitis, the most likely cause of fever is a bacterial infection of the gallbladder. The patient's poorly controlled diabetes (HbA1c of 13) increases the risk of infections, including those of the gallbladder.

Sepsis secondary to another source: Although the focus is on acalculus cholecystitis, the patient's high fever and chills could also indicate sepsis originating from another source, such as a urinary tract infection, pneumonia, or a skin infection, which are common in elderly patients, especially those with diabetes.
Diabetic ketoacidosis (DKA) or hyperglycemic hyperosmolar nonketotic syndrome (HHNS): Poorly controlled diabetes can lead to these conditions, which may present with fever, although they are not infections per se. The high HbA1c level suggests a possibility of these metabolic emergencies.

Endocarditis: Although less likely, infective endocarditis can present with fever and systemic symptoms and is a diagnosis that should not be missed due to its high mortality rate if untreated. The presence of chills could suggest bacteremia.
Intra-abdominal infection other than cholecystitis: Other abdominal infections, such as diverticulitis or perforated viscus, could present similarly and require urgent surgical intervention.

Fungal infection: In immunocompromised patients, such as those with very poorly controlled diabetes, fungal infections can occur, including fungal cholecystitis, although this is much less common than bacterial causes.
Malignancy: Rarely, a malignancy involving the gallbladder could present with fever and chills, although this would be an uncommon initial presentation.