For run of the mill sinus infections I have used mupirocin ointment (Rx only) directly applied into the nostrils 3x day for 2 weeks. I do not know if it would treat pseudomonas. Be careful with its use as it should not be used more than 2-3 per year.

It's easy to recontaminate your sinuses with your rinse bottle. NeilMed bottles are not easy to sterilize. This might be a reason you are getting recurrent infections. From advice on this forum I switched to NeilMed's Squeezie. It's easier to use than the regular squeeze bottle and easier to clean. I pop it in my baby bottle sterilizer every 2 days after cleaning it up a drop of Dawn. Or you could buy a ceramic Neti pot which could be boiled.

While you are having this infection you might use Hibiclens to wash your hands. You can use it around/outside of nose not inside. Changing the pillowcase daily also been recommended to me.