Normally prohibited as a tolda (derivative) of the av malacha (main category of work) shochet (slaughter) drawing blood is forbidden by the Torah. If someone were taking an injectable medication/supplement several times each day and thus it would be unavoidable on shabbos unless he/she suspended using it altogether on that day under what circumstances would it be allowed to be used on shabbos? Would it only be permitted if not using it was life threatening? What if it wasn't life threatening but stopping for a day would make it less effective?
According to Rav Ovadia Yosef, one would indeed be permitted to continue a course of antibiotics or any course of medication one had started taking prior to Shabbat.
This article on Rav Ovadia Yosef's ruling quotes Hagaon Harav Shlomo Kluger as stating that since one had begun the course of medication beforehand, there is no concern of having to prepare the medication on Shabbat itself.
There does not appear to be a difference in this matter between pills and injectables; an injection is very different from bloodletting.