NFHS and NCAA Rules are quite specific: No jewelry for the players!
That said, game officials are a different animal. Until the late 1980's, game officials could wear only a wedding ring (nothing was said about engagement rings), then without any editorial comment, the CCA Manual stated that not even a wedding ring could be worn by the game officials.
Therefore, an official can wear a wedding ring while officiating H.S. game but cannot wear a wedding ring for a college game.
MTD, Sr.
P.S. Since I had been officiating for a number of years before I married my wonderful wife, I have always removed my H.S. (then my college ring) when officiating and I even removed my Engineer's Ring when officiating, and I still remove my wedding ring when officiating.