If the well used antibiotic kills all bacteria which participate in infection e.g. sinus infection?

Question: Question unclear. Antibiotics normally prescribed for sinusitis work well in killing pathogenic bacteria.

Not sure understand: your question. There is no antibiotic which kills all bacteria. Sinusitis can be caused by viruses, in which case antibiotics will not help. Bacteria which most commonly cause sinus infection, include: Streptococcus pneumoniae, Haemophilus influenzae, and Moraxella catarrhalis. Antibiotics commonly used to treat sinus infections include Augmentin, (amoxicillin and clavulanate) Zithromax, Bactrim (Septra), and levoquin.