IMO stop your fast if you are starting to get sick. I also am starting to get cold/flu symptoms and am relaxing my OMAD by adding a teaspoon of honey to my morning tea (giving my immune system readily available energy) and I wont fast until I feel I’m over it (unless if I’m actually not hungry that is).
Fasting during a cold is fine. The body naturally wants to do this, ask any parent of a kid who loses their appetite when sick. The supplement might kick you out of ketosis, but probably not as it looks like only 20 calories.