For my father, Betadine was prescribed by the Radition Doc, so I do not see any issue in using it post-rad for you. Swish it as long as you feel like so that it reaches everywhere and long enough to kill all microbes in your mouth.

My dad had a review today and the thrush seems to have come back for him so doc gave him Candid Mouth Paint to apply three times a day to get rid of it.