[12] On August 20, the first day of competition at the 2019 World Junior Championships in Budapest, Hungary, Matheny broke the National Age Group record for the boys 15–16 age group in the 100 meter breaststroke with a time of 1:00.66 that lowered the record set by Michael Andrew in 2015 by two-hundredths of a second.

[13][14] Later in the day, Matheny broke his own record with a time of 1:00.32 in the semifinals of the 100 meter breaststroke, advancing to the final ranking first overall.

[15][16] The next day, August 21, in the final of the 100 meter breaststroke Matheny broke his own record again, swimming a 1:00.17 to win the silver medal in the event only behind Vladislav Gerasimenko of Russia.

[24] Additionally, he became the fifth American male swimmer aged 18 years old or younger to swim the event in less than one minute, fifty-two seconds flat, after Kevin Cordes in 2012, Andrew Seliskar in 2015, Reece Whitley in 2017, and Daniel Roy in 2018.

[33][34] Swimming the breaststroke leg of the 4×50 yard medley relay in 23.43 seconds on the first day of the 2022 Big Ten Conference Championships in February, Matheny helped achieve a time of 1:22.51 and second-place finish.

[36] Later in the day, during the evening finals session, he split a 50.76 for the breaststroke leg of the 4×100 yard medley relay to help achieve a first-place finish in a Championships record time of 3:00.95.

[37][38] The third day of the Championships, Matheny swam a 52.13 in the prelims heats of the 100 yard breaststroke to qualify for the final ranking fifth, just 0.11 seconds behind the first-ranked swimmer.

[46] At the 2022 US International Team Trials in Greensboro, North Carolina in late April, Matheny ranked eighth and qualified for the final of the 200 meter breaststroke with a time of 2:14.41 in the prelims heats on the morning of day two.

[54] In a dual meet against the Michigan Wolverines in January 2023 and leading up to the collegiate championships season, Matheny achieved a win in the 200 yard breaststroke with a time of 1:59.54.

[56] Starting his sophomore (second year) Big Ten Conference Championships on day two of competition, February 23, he helped win the conference title in the 4×100 yard medley relay with a Canham Natatorium pool record of 3:01.53 by swimming the 100 yard breaststroke portion of the relay in 50.77 seconds.

[57][59] Concluding the Championships on day four with the 200 yard breaststroke, he won the silver medal in a time of 1:51.23, finishing 1.03 seconds behind gold medalist Max McHugh, and contributing to an overall team title win for the Indiana Hoosiers.

[61] In the evening final, he placed fourth in a personal best time of 1:50.12, finishing 3.21 seconds behind gold medalist Léon Marchand of the Arizona State Sun Devils.