Jelkin attended Bellevue West High School in Nebraska. He held a 1.20 ERA with 80 strikeouts over 52.1 innings as a senior. He earned All-State Honors and decided to join Nebraska.
As a freshman with the Huskers, Jelkin pitched out of the bullpen, making 6 appearances and just 1 start. He had a 2.31 ERA with 9 strikeouts and 7 walks in 11.2 innings pitched.
Jelkin transferred to South Mountain Community College for his sophomore season. He held a 3.81 ERA, and led the team with 98 strikeouts over 75.2 innings. He posted a 7-2 record in his 14 starts, and gained interest as he entered the transfer portal again following his sophomore year.
Jelkin transferred to Houston for his junior season this year, and has been talked about as a potential draft prospect with a solid performance this year.