Does it make sense depleting immune system with active infection and no antibiotic?


65 year old male former smoker
best begin with my language barriers with staff at local Thailand hospital.
treated for “bacterial lung infection” determined from blood presumably was pneumonia January 1
5 days intravenous antibiotic 1 x per day for 5 days + regimen Sudafed, Ambroxol.
Breathing difficulty never really seemed to clear.
Recently sustained “minor cold” about 2 weeks ago that with coughed mucous turning greener returned to hospital.
This time prior to reviewing chest x-ray taken doctor had me on nebulizer for 3 vials and perhaps miscommunicated intention of another antibiotic intravenous regime, because the only thing close was one injection of something in my hand.
I see the doctor again after presumably reviewing the x-ray
Prescribed Advair 2x per day, Berodual inhaler for any serious breathing difficulty.
Ambroxol 30 mg tablet 3x daily
Zertec 10 mg 1/ day
PREDNISOLONE 10 mg. 3x daily, but NO ANTIBIOTIC.
This morning coughing not as frequent, but mucous turning greener.
Question does it make sense depleting immune system with active infection and no antibiotic

Age: 65
Medications: Prednisolone, Ambroxol, Zytrec, Advair
General Information: Biggest question is possible error being prescribed a medication depleting the immune system with an active lung infection but no antibiotic.