|Don't do it. Abuse and misuse of antibiotics is causing a major headache for the medical community. There are many more "bugs" now resistant to antibiotics than ever before. Antibiotics are for bacterial infections. A urushiol induced rash (poison ivy rash) is an allergic reaction. Only if you have an infection should antibiotics be considered.
Here's a good read about antibiotics:
Antibiotics - The Untold Story
That said - perhaps you should review why you are getting an annual affliction. Reinfection? Not recognizing the plant?