Giallanza played youth football with Old Boys and joined OB's first team for their 1991–92 in their Nationalliga B season. The following season he played with Basel U-18 team and had one appearance for their first team in Basel's 1992–93 season, also in the second tier of Swiss football. Giallanza moved on and signed for Servette in the 1993–94 Nationalliga A season. Servette won the championship and Giallanza scored one goal in ten appearances. He again moved on and signed for Young Boys for the 1994–95 Nationalliga A season. YB finished the qualification round bottom of the table and slipped into the relegation round. In the relegation round Giallanza scored nine goals and helped save the team from relegation. With the seven goals from the qualifying round, he was the team’s top goal scorer. Giallanza played the following season with Sion, but could not maintain a place in the starting eleven and so moved on again.
