Feltman attended and graduated from Oak Ridge High School in Conroe, Texas, alongside Luken Baker.

[13] He was assigned to the Class A Short Season Lowell Spinners, and made his professional debut on June 29.

On July 10, Feltman was promoted to the Class A Greenville Drive,[16] where he made seven one-inning appearances, compiling a 2.57 ERA while striking out 14 and walking one.

[18] On August 1, Feltman was promoted to the Class A-Advanced Salem Red Sox, where he finished the season.

[19] Feltman spent 2019 with the Portland Sea Dogs of the Class AA Eastern League, going 2–3 with a 5.26 ERA over 43 relief appearances, striking out 54 over 51+1⁄3 innings.

[21] To begin the 2021 season, he returned to Portland (now members of the Double-A Northeast), and was promoted to the Worcester Red Sox of the Triple-A East in late July.

[26] On April 18, 2023, Feltman signed a minor league contract with the Oakland Athletics organization and was assigned to the Double-A Midland RockHounds.