Brief Answer:
Oral is better, topical care as side therapy

Detailed Answer:
Thank you for asking!
Pseudomonas is a strictly aerobic, gram-negative bacterium of relatively low virulence. The organism is ubiquitous, with a predilection to moist environments, primarily as water borne and soil borne organisms. Pseudomonas species have been found in soil, water, plants, and animals;.These organism most of the time show resistant to antibiotics but there might be the chance you may be misdiagnosed and there might be some other nasal infection like Staph aureus etc responsible for this.
Two antipseudomonal drug combination therapy (eg, a beta-lactam antibiotic with an aminoglycoside) is usually recommended and works like charm to almost all pseudomonas species.Usually when the infection occurs in nasal area it involves nearby ear too and cause otitis media and externa which may need surgical intervention. If the above mentioned therapy fails then next one is Carbapenems (eg, imipenem, meropenem) and the monobactam antibiotic aztreonam they are generally reserved for serious infections caused by organisms resistant to other beta-lactam antibiotics or in those with renal disease who are at risk for aminoglycoside-related nephrotoxicity. I believe you can be qualified for that as per your resistance.
Now the main query of any topical application so i am afraid that won't be possible in antibiotics as they lead to resistance in organisms. Oral is better. You can treat symptoms of nose with tropical hygiene agents for nasal troubles but antibiotics got to be taken oral or IV. Rest nasal hygiene can help reduce the organisms load so that is not forbidden. There are a few topical antibiotics available mostly macrolides.
But i suggest you seek an infectious disease specialist and an otorhinolaryngologist for a complete assessment and reconsidering the diagnosis and sort out the issue for the resistance.
I hope it helps. Dont forget to close the discussion please.
Take care
S Khan

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