the chance of recurrence is much higher, much higher than the chance of getting lung cancer or leukemia.
I_131 mainly concerntrates in thyroid tissue. If you do not spill while taking I_131, you do not need to give up your personal belongings. However, you shoud not hold babies for a few weeks as they can get radiation from I-131 around your neck. Half life of I_131 is about 8 days. Good luck.