This is obviously a significant concern for you. So you should talk with your doctor about it. Having chronic leukemia means you will need to have confidence in your doctor and the decisions he/she makes for you.
Pneumonia usually causes acute symptoms, such as coughing, fever and sometimes difficulty breathing. Often, after antibiotics the infection gets better but it takes longer for all the symptoms to go away. If you did not tell your doctor that you are still coughing, then he/she may think that the antibiotic that you were given took care of the cough and that you are all right. If you are continuing to feel lethargic and if the coughing is not going away or if it is getting worse, I would suggest going back to your doctor. Then you can see if you need a new antibiotic, need to continue on the same one, or need to see a lung specialist.
For persistent pneumonia it would be best to be seen by a pulmonologist.