What determines if I need rai treatment after thyroidectomy? I have two nodules which are pappilary thyroid cancer.

Depends. Most of the time after thyroidectomy recurrences are treated with rai , but not always younger people surical removal is preferred choice , you have to discuss with your oncology team which is the best method for that particular person.
Size and features. It depends upon the size and pathologic features of the tumor. Small noninvasive papillary cancers may not benefit from use of radioiodine. Check w/your endocrinologist.