On October 1, Barajas made his professional debut for the Battery in their 6–3 defeat at Hartford Athletic, coming on as a 71st-minute substitute and recording one assist.[3] He made his first start on October 8 against Indy Eleven, registering another assist in the 4–1 loss.[4] Barajas made three total appearances in 2022.
On March 25, 2023, Barajas scored his first professional goal in a 3–0 win over the Tampa Bay Rowdies, in the 3rd minute, and also added an assist in the second half. He was subsequently named to the USL Championship Team of the Week for his performance against Tampa Bay.[5]
Barajas entered the league record books on July 22, 2023, with a two-assist match against Pittsburgh Riverhounds SC, becoming the fourth-youngest player to achieve the feat. He turned in another noteworthy performance on September 23 against FC Tulsa with the first brace of his professional career, becoming the ninth-youngest player in league history to record a two-goal game.[6] He ended the regular season with four goals and nine assists, the latter being one away from the league lead, and was named Players' Choice Young Player of the Year by the USL Players Association.[7]
On 11 October 2023, he was named by English newspaper The Guardian as one of the best players born in 2006 worldwide.[8]
In the 2023 USL Championship Playoffs, Barajas scored one goal and one assist in the opening round, a 5–0 defeat over Indy Eleven on October 22. He recorded another assist in the following round, a 2–1 win over Birmingham Legion FC, bringing his total to 11, the most in the league across the regular season and playoffs in 2023. That mark also tied a club record for assists in a single season, matching Temoc Suarez's tally of 11 in 2000, set six years before Barajas was born.
Barajas was named the USL Championship All-League Second Team and won USL Championship Young Player of the Year after the season ended.[9][10]
Barajas has represented both the United States and Mexico youth national teams.[2]
Barajas competed in a UEFA Development Tournament in May 2022 with the USYNT, playing against the youth squads of Portugal, Italy and Belgium. He tallied an assist in the match against Belgium, a 0–3 victory, and also played against the youth teams of Argentina and Uruguay.
For Mexico, Barajas played for the Mexico U-17's at the International Dream Cup in Japan in June 2022. He featured in matches against Japan, South Korea, and Uruguay, scoring one goal against South Korea and contributing two assists against Uruguay.[14] Barajas rejoined Mexico in October 2022 for the UNCAF FIFA Forward U-16 Tournament in Honduras. Fidel appeared in all four matches, scoring one goal and contributing four assists, as Mexico ended as runners-up in the tournament final.[15]
Barajas was selected for the 2023 CONCACAF U-17 Championship by Mexico and helped lead them to win the tournament. He started all seven matches and contributed three goals and five assists. He played 74 minutes in the final, against the U.S., and had a hand in setting up two of Mexico's three goals to lift the trophy in Guatemala City. In addition to winning the title, Barajas and Mexico earned qualification for the 2023 FIFA U-17 World Cup in Indonesia in the following November.[16]