I am prescribed a medication that has multiple purposes. Originally I was prescribed it to address a skin rash. I then developed another issue that affects my breathing and the same medicine helps to ease breathing. Originally I didn’t take it during Shabbos. May I now take it on Shabbos and Yom Tov?
As the prolonged interruption can adversely affect the breathing.
It is hard for me to understand what you mean, by prolonged interruption of the medication, if you mean by not taking it on Shabbos, or for longer periods than that. If your abstaining from taking the medication on Shabbos is going to adversely affect your breathing, then it is permitted to take it.