Hi! I think you should go ahead with the antibiotics although I am not familar with the one you mentioned. Is it like doxycylin or Bactrim? These are two oral abx that are used regularly in the US for staph. Does she not culture PA too though? I ask because it is usually necessary to treat both.
Don't worry about resistance. Get her back to NO COUGH otherwise permanent lung damage may occur. My son's clinic won't let him cough for 4 (FOUR) days without starting him on a 14 day course of oral abx.
Get her healthy because as you know great things are around the corner to treat this hideous disease and you want her to be in the best shape possible.