I have this and yes it can, IF you become colonized with it. I have it in my sinuses. Treated with antibiotics does not always mean cured.
I noticed you mentioned getting your teeth checked and cleaned. What is the connection with teeth? My daughter had Osteomyelitis Pseudomona in her neck last summer. The pain started the day after she had 4 wisdom teeth extracted. I was wondering if their is a connection?
Your doctor should culture your sinuses and do specific blood work regarding this infection. If you have post nasal drip it will get into your lungs. You should see an immunologist/allergist asap. IV cefepime is the newest medication that is bactericidal. Additionally, you may need an oral antifungal to prevent yeast/fungus. The IV medication can be done 2x daily via a PICC line for 4,6 or up to 8 wks if necessary. You should be recultured. This is a difficult bacteria to get rid of once you have it. Get your teeth checked/cleaned and rinse out your sinuses as often as possible with warm saline solution. Good luck.