Will Cetraxal be effective for ear infection with Pseudomonas aeruginosa and Staphylococcus aureus?

The daughter of 6 years for almost a year scratches her ears and her earwax stinks. One ENT man claimed that he was all ok, he gave anti-histamine drugs. Another doctor said that everything was ok in the air and it was probably allergic. After a while, we were at the other ENT again, he still thought it was ok, but just in case he made a swab from the ear. It came out that the daughter has bacteria: pseudomonas aeruginosa and staphylococcus aureus. I don't have an overview of the results with an ENT doctor until March 22, but so as not to wait, I consulted the pediatrician who prescribed us cetraxal. Has the drug been properly selected and is there a chance that after this treatment we will get rid of the problem with the uszami? Is there anything I should know about these bacteria, treatment? The pediatrician concluded that this bacterium first is very dangerous.