While rounding with one of our pediatric pulmonologists:
It often takes 6-8 weeks before someone with obstructive sleep apnea recovers enough from tonsillectomy & adenoidectomy to be eligible for repeat sleep study. Follow-up with pulmonology in two months. If they had problems with low oxygen saturation overnight, consider discharge with home oxygen for sleep, though then they will need to have a sleep study to document that they can stop that.
Abbreviations: T&A, OSA