Geli obtained her medical degree from the University of Barcelona. She was an intern at the Hospital Josep Trueta in Girona from 1981 to 1990. She became a specialist in the treatment of infectious diseases and AIDS. She was also involved in several associations related to the fight against AIDS.
She also was town councillor for Sant Gregori (1982–1990) and county councillor for Girona, during the same period.
She is president of the Committee for Social Policy in the period 1996-1999 in the Catalan Parliament and Spokesperson for Social Policy in the sixth legislature.
She became policy manager and First Secretary of the PSC for the region of Girona in 2000.