There are few important possibilities here.
First the current infection is most likely to be due to a resistant bug which does not respond adequately to the antibiotics prescribed to her and resultantly, it has failed to be eradicated from her respiratory tract.
For this purpose, she should have a culture test done (of the phlegm) and the doctor may also consider bronchoscopy (a tube passed in the lungs) and lavage (washings taken from the lungs during bronchoscopy) and subject them for a culture test as well.
This test will help identify the bug responsible for the infection and will also direct the use of specific antibiotics that will work best against that bug.
Another possibility is Post-Infectious bronchial hyper-reactivity syndrome. This condition occurs after an infection is over and present with ongoing cough, phlegm and shortness of breath (just like asthma). But the good thing about this is that this lasts only for few weeks or even months at times, and responds well to bronchodilator drugs and inhalers which can be stopped later on when the symptoms settle down.
Finally, a repeat chest X-ray should be done, and sputum/phlegm should also be sent for AFB stain (a special staining for phlegm to detect tuberculosis bug which is not usually detected in routine cultures) to rule out tuberculosis.
At this point, she should see a Pulmonologist and discuss all these details i have mentioned to chalk out further management plan that suits best to her needs.
Daily steam inhalation.
Plenty of water intake (that helps to loosen out the phlegm) will be helpful.
Wish you good luck.
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I would have been worried too if i were at your place but let me reassure you that this is a treatable condition and carry a good prognosis with appropriate management.