Regular staph infection in the nose can transmit to other body parts, so be sure to wash your hands thoroughly after you blow your nose.
I was advised by my pharmacist to prevent the spread of staph from my nose and to help get rid of it, to use Bacitracin cream, a very light coating inside nostrils, once or twice a day.
Ask your pharmacist or doctor. Tell them that you are on Bactrim and see if they think this might be helpful.
Lindaru