Although he seemed destined to be one of the mainstays of Celta de Vigo, Luis Otero, along with two other players - Chiarroni and González -, not satisfied with the discipline of the new club, left the entity before the start of the 1923 Galician Championship to sign for Deportivo de La Coruña, which ultimately proved to be one of the triggers of the historical rivalry between the Vigo and Coruña teams.

[citation needed] On 28 August 1920, Otero went down in history as one of the eleven footballers who played in the first game of the Spanish national team at the 1920 Summer Olympics, in an eventual 1–0 victory over Denmark.

[9] He also featured in the second round of the repechage tournament against Italy which Spain won 2–0, winning the silver medal three days later after beating the Netherlands 3–1, making Otero and Moncho Gil the first Galician Olympic medalists in history.

In total, he earned four caps for Spain, two at the 1920 Olympics and two in friendlies, the last of which was on 21 December 1924 at Les Corts in a 2–1 win over Austria.

[10] Being a player of Real Vigo Sporting, he was summoned to play for the Galicia national team, and he was one of the eleven footballers that played in the first game of the team's history, a 4–1 win over a Castile/Madrid XI in the quarter-finals of the 1922-23 Prince of Asturias Cup, an inter-regional competition organized by the RFEF.