Phelps, of Baltimore, finished second to Schooling in the 100 fly, in which the 18-time Olympic gold medalist holds the world record. Schooling, a 20-year-old University of Texas swimmer, won in 51.58 seconds. Phelps' time was 51.65.
Phelps finished in 49.49 in the 100 freestyle to beat Conger, another Texas swimmer.
The Longhorn meet is one of three around the country for elite swimmers this weekend ahead of the U.S. Olympic Trials at the end of the month.
Arena Pro Swim Series events are being held in Santa Clara, Calif., and Indianapolis through Sunday. The trials are June 26-July 3 in Omaha, Neb.