@betsey Pseudomonas infections are considered "opportunists" so if you have primary immunodeficiency, it can crop up in many places. Sinuses are definitely one of them.
Unfortunately, pseudomonas is slow to respond to treatment, but for sinus involvement Tobramycin rinse is considered the "gold standard." When it was in my lungs, each antibiotic was used for at least 4 weeks before reevaluation - it took 3 months to conquer.
So I would say you need to have a little patience, but if you don't begin to feel better after 3 weeks, it is probably time for a test of the sensitivity of your strain - a second oral or injected antibiotic might need to be added. That has it's own downside because these can have their own side effects.
Are you seeing an ENT ot ID doc for this?
Sue