The use of phytogenic extracts is considered a sustainable strategy for the prevention of fish diseases, including Alliaceae as a potential option due to their variety of bioactive compounds. In this study, we analyzed the antibacterial and antiparasitic potential of propyl-propane-thiosulfinate (PTS) and propyl-propane-thiosulfonate (PTSO) from onions. The in vitro activity against Pseudomonas anguilliseptica, Tenacibaculum maritimum, and Photobacterium damselae of both compounds was tested. In addition, the viability of Sparicotyle chrysophrii larvae was evaluated. Moreover, a diet that consisted of a blend of PTS/PTSO (ALLIUM) was used. A total of 90 gilthead sea bream juveniles were tested against P. damselae subsp. Piscicida after 12 weeks of dietary administration. Furthermore, 150 fish with a rate of 10–15 parasites/fish were fed for 21 days and the number of gill parasites was recorded. All strains were sensitive to both compounds. PTSO showed the highest inhibitory effect against all target strains, while PTS showed higher effectiveness against S. chrysophrii. Fish from ALLIUM group presented the highest probability of survival, increasing up to 91.1%, whereas in the control group, the probability of survival was 66.7%. The number of parasites in the gilthead sea bream decreased in the ALLIUM group over time. These results suggest the inclusion of PTS and PTSO in feed as a natural strategy to prevent antibacterial and antiparasitic fish diseases.