You have indicated that you have had a >3 week illness, involving the abdomen and chest and that you continue to have bad back pain, cough, fever, sweats and fatigue, but your “stomach is better”. The back and flank pain, if not pleuritic pain (from pleurisy associated with pneumonia) is worrisome for disease of organs in that part of your body; that is, your kidneys and pancreas. Was there a complete (not just the CT Scan) absence of evidence for recurrent pancreatitis; you may want to ask your doctor about that. And, have they looked to your kidneys as the main site of disease, conceivably with a perinephric abscess. This latter usually presents with fever, abdominal and flank pain, but presenting symptoms can be non-specific, with fever persisting after two weeks or more. About 1/3 of persons with an abscess have no signs of infection in their urine. Your doctors might want to consider repeating the CT Scan.
And, to answer your question, the presence of an abscess could explain your less than expected response to antibiotics. And, with septicemia (bacteria in your blood), could also account for the pneumonia.
That you are still ill, with fever and sweats is a reason for your doctors to conduct an extensive search for a primary site of infection, including your heart for an infection called sub-acute or acute bacterial endocarditis. At this point you should also request consultation with an Infectious Disease Specialist, if one is not already involved in your care.
Good luck