I use pulmicort in my nasal rinse-- should i gargle and rinse my mouth afterwards?

Yes: When uses any nasal steroids then rinsing of the mouth afterwards can be helpful to minimize the risk of thrush.

Yes: Not a bad idea. The goal would be to wash out any excess pulmicort/budesonide/steroid out of your mouth and throat - where it is not needed. Although i will say i commonly prescribe the Budesonide in nasal rinse, don't usually remind patients to rinse their mouth afterwards, and have not seen problems. Typically if the nasal rinse goes out in one nostril and out the other, your mouth is fine.