Actually, the Full Moon in July occurred on July 30th at 10:36 UT. The last Full Moon on July 23rd was either on July 24 1983 at 23:27 UT or July 23 at 5:29 UT, and it depends on which time zone you are in as to which is the closest to your date. The next Full Moons on or near the 23rd are:
July 24 2002 at 9:08 UT July 22 2013 at 18:16 UT July 24 2021 at 18:16 UT July 22 2032 at 18:52 UT July 24 2040 at 2:06 UT July 22 2043 at 3:25 UT.