Alshammar was a part of the Swedish team in 1993 European Championships in Sheffield, finishing fourth in the 100 m backstroke final, and in the inaugural World Short Course Championships in Palma de Mallorca. In Palma de Mallorca she took a ninth place in the individual 100 m backstroke, swum the prelims in the silver medal winning 4×100 m freestyle team and came fourth in the 4×100 m medley alongside breaststroker Hanna Jaltner, butterfly swimmer Ellenor Svensson and Linda Olofsson on the freestyle leg.